LMFDB - Embedded newform 441.2.g.b.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.3
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	441.67
Dual form			441.2.g.b.79.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.439693 - 0.761570i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} -1.34730 q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})$	\(q+(0.439693 - 0.761570i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} -1.34730 q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +(-0.592396 + 1.02606i) q^{10} +1.65270 q^{11} +(-0.726682 + 1.99654i) q^{12} +(-1.68479 + 2.91815i) q^{13} +(-1.50000 - 1.78763i) q^{15} +(0.0209445 - 0.0362770i) q^{16} +(0.233956 - 0.405223i) q^{17} +(2.02094 + 1.69577i) q^{18} +(-1.61334 - 2.79439i) q^{19} +(-0.826352 - 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +8.94356 q^{23} +(3.15910 + 3.76487i) q^{24} -3.18479 q^{25} +(1.48158 + 2.56617i) q^{26} +(-4.50000 + 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(-2.02094 + 0.356347i) q^{30} +(4.61721 + 7.99724i) q^{31} +(2.81908 + 4.88279i) q^{32} +(1.84002 + 2.19285i) q^{33} +(-0.205737 - 0.356347i) q^{34} +(-3.45811 + 1.25865i) q^{36} +(-4.61721 - 7.99724i) q^{37} -2.83750 q^{38} +(-5.74763 + 1.01346i) q^{39} -3.82295 q^{40} +(1.70574 - 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +(1.01367 + 1.75573i) q^{44} +(0.701867 - 3.98048i) q^{45} +(3.93242 - 6.81115i) q^{46} +(4.67752 - 8.10170i) q^{47} +(0.0714517 - 0.0125989i) q^{48} +(-1.40033 + 2.42544i) q^{50} +(0.798133 - 0.140732i) q^{51} -4.13341 q^{52} +(0.286989 - 0.497079i) q^{53} +4.56942i q^{54} -2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} -5.51249 q^{58} +(-5.19846 - 9.00400i) q^{59} +(0.979055 - 2.68993i) q^{60} +(3.81908 - 6.61484i) q^{61} +8.12061 q^{62} +5.04189 q^{64} +(2.26991 - 3.93161i) q^{65} +(2.47906 - 0.437124i) q^{66} +(-0.298133 - 0.516382i) q^{67} +0.573978 q^{68} +(9.95723 + 11.8666i) q^{69} -0.554378 q^{71} +(-1.47818 + 8.38316i) q^{72} +(1.02481 - 1.77503i) q^{73} -8.12061 q^{74} +(-3.54576 - 4.22567i) q^{75} +(1.97906 - 3.42782i) q^{76} +(-1.75537 + 4.82283i) q^{78} +(1.20187 - 2.08169i) q^{79} +(-0.0282185 + 0.0488759i) q^{80} +(-8.45723 - 3.07818i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-7.52481 - 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +3.87939 q^{86} +(3.71348 - 10.2027i) q^{87} +4.68954 q^{88} +(4.54323 + 7.86911i) q^{89} +(-2.72281 - 2.28471i) q^{90} +(5.48545 + 9.50108i) q^{92} +(-5.47044 + 15.0299i) q^{93} +(-4.11334 - 7.12452i) q^{94} +(2.17365 + 3.76487i) q^{95} +(-3.34002 + 9.17664i) q^{96} +(-0.949493 - 1.64457i) q^{97} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 9 * q^6 + 12 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 9 q^{6} + 12 q^{8} + 12 q^{11} + 9 q^{12} - 3 q^{13} - 9 q^{15} - 3 q^{16} + 6 q^{17} + 9 q^{18} - 3 q^{19} - 6 q^{20} - 9 q^{22} + 24 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 27 q^{27} - 9 q^{29} - 9 q^{30} - 3 q^{31} - 9 q^{33} + 9 q^{34} - 27 q^{36} + 3 q^{37} - 12 q^{38} - 18 q^{39} + 18 q^{40} + 3 q^{43} - 15 q^{44} + 18 q^{45} + 3 q^{47} + 6 q^{50} - 9 q^{51} + 42 q^{52} - 6 q^{53} - 9 q^{57} - 18 q^{58} - 3 q^{59} + 9 q^{60} + 6 q^{61} + 60 q^{62} + 24 q^{64} - 15 q^{65} + 18 q^{66} + 12 q^{67} - 12 q^{68} + 9 q^{69} + 18 q^{71} + 45 q^{72} - 21 q^{73} - 60 q^{74} + 9 q^{75} + 15 q^{76} + 54 q^{78} + 21 q^{79} - 15 q^{80} - 9 q^{82} - 18 q^{83} - 9 q^{85} + 12 q^{86} - 36 q^{87} + 54 q^{88} + 12 q^{89} - 27 q^{90} - 3 q^{92} - 27 q^{93} - 18 q^{94} + 12 q^{95} - 3 q^{97} + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 9 * q^6 + 12 * q^8 + 12 * q^11 + 9 * q^12 - 3 * q^13 - 9 * q^15 - 3 * q^16 + 6 * q^17 + 9 * q^18 - 3 * q^19 - 6 * q^20 - 9 * q^22 + 24 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 27 * q^27 - 9 * q^29 - 9 * q^30 - 3 * q^31 - 9 * q^33 + 9 * q^34 - 27 * q^36 + 3 * q^37 - 12 * q^38 - 18 * q^39 + 18 * q^40 + 3 * q^43 - 15 * q^44 + 18 * q^45 + 3 * q^47 + 6 * q^50 - 9 * q^51 + 42 * q^52 - 6 * q^53 - 9 * q^57 - 18 * q^58 - 3 * q^59 + 9 * q^60 + 6 * q^61 + 60 * q^62 + 24 * q^64 - 15 * q^65 + 18 * q^66 + 12 * q^67 - 12 * q^68 + 9 * q^69 + 18 * q^71 + 45 * q^72 - 21 * q^73 - 60 * q^74 + 9 * q^75 + 15 * q^76 + 54 * q^78 + 21 * q^79 - 15 * q^80 - 9 * q^82 - 18 * q^83 - 9 * q^85 + 12 * q^86 - 36 * q^87 + 54 * q^88 + 12 * q^89 - 27 * q^90 - 3 * q^92 - 27 * q^93 - 18 * q^94 + 12 * q^95 - 3 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.439693	−	0.761570i	0.310910	−	0.538511i	−0.667650	−	0.744475i	$-0.732700\pi$
$2$	0.439693	−	0.761570i	0.310910	−	0.538511i	0.978560	+	0.205964i	$0.0660330\pi$
$3$	1.11334	+	1.32683i	0.642788	+	0.766044i
$3$	1.11334	+	1.32683i	0.642788	+	0.766044i
$4$	0.613341	+	1.06234i	0.306670	+	0.531169i
$5$	−1.34730			−0.602529			−0.301265	−	0.953541i	$-0.597409\pi$
$5$	−1.34730			−0.602529			−0.301265	+	0.953541i	$0.597409\pi$
$6$	1.50000	−	0.264490i	0.612372	−	0.107978i
$7$		0			0
$7$		0			0
$8$	2.83750			1.00321
$9$	−0.520945	+	2.95442i	−0.173648	+	0.984808i
$10$	−0.592396	+	1.02606i	−0.187332	+	0.324469i
$11$	1.65270			0.498309			0.249154	−	0.968464i	$-0.419847\pi$
$11$	1.65270			0.498309			0.249154	+	0.968464i	$0.419847\pi$
$12$	−0.726682	+	1.99654i	−0.209775	+	0.576352i
$13$	−1.68479	+	2.91815i	−0.467277	+	0.809348i	−0.999301	−	0.0373813i	$-0.988098\pi$
$13$	−1.68479	+	2.91815i	−0.467277	+	0.809348i	0.532024	+	0.846729i	$0.321432\pi$
$14$		0			0
$15$	−1.50000	−	1.78763i	−0.387298	−	0.461564i
$16$	0.0209445	−	0.0362770i	0.00523613	−	0.00906925i
$17$	0.233956	−	0.405223i	0.0567426	−	0.0982810i	−0.836259	−	0.548335i	$-0.815262\pi$
$17$	0.233956	−	0.405223i	0.0567426	−	0.0982810i	0.893001	+	0.450054i	$0.148595\pi$
$18$	2.02094	+	1.69577i	0.476341	+	0.399698i
$19$	−1.61334	−	2.79439i	−0.370126	−	0.641077i	0.619459	−	0.785029i	$-0.287352\pi$
$19$	−1.61334	−	2.79439i	−0.370126	−	0.641077i	−0.989585	+	0.143953i	$0.954019\pi$
$20$	−0.826352	−	1.43128i	−0.184778	−	0.320045i
$21$		0			0
$22$	0.726682	−	1.25865i	0.154929	−	0.268345i
$23$	8.94356			1.86486			0.932431	−	0.361348i	$-0.117683\pi$
$23$	8.94356			1.86486			0.932431	+	0.361348i	$0.117683\pi$
$24$	3.15910	+	3.76487i	0.644849	+	0.768501i
$25$	−3.18479			−0.636959
$26$	1.48158	+	2.56617i	0.290562	+	0.503268i
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$		0			0
$29$	−3.13429	−	5.42874i	−0.582022	−	1.00809i	−0.995239	−	0.0974595i	$-0.968928\pi$
$29$	−3.13429	−	5.42874i	−0.582022	−	1.00809i	0.413217	−	0.910632i	$-0.364405\pi$
$30$	−2.02094	+	0.356347i	−0.368972	+	0.0650598i
$31$	4.61721	+	7.99724i	0.829276	+	1.43635i	0.898607	+	0.438754i	$0.144580\pi$
$31$	4.61721	+	7.99724i	0.829276	+	1.43635i	−0.0693317	+	0.997594i	$0.522087\pi$
$32$	2.81908	+	4.88279i	0.498347	+	0.863163i
$33$	1.84002	+	2.19285i	0.320307	+	0.381727i
$34$	−0.205737	−	0.356347i	−0.0352836	−	0.0611130i
$35$		0			0
$36$	−3.45811	+	1.25865i	−0.576352	+	0.209775i
$37$	−4.61721	−	7.99724i	−0.759065	−	1.31474i	−0.943328	−	0.331862i	$-0.892323\pi$
$37$	−4.61721	−	7.99724i	−0.759065	−	1.31474i	0.184263	−	0.982877i	$-0.441010\pi$
$38$	−2.83750			−0.460303
$39$	−5.74763	+	1.01346i	−0.920357	+	0.162284i
$40$	−3.82295			−0.604461
$41$	1.70574	−	2.95442i	0.266391	−	0.461403i	−0.701536	−	0.712634i	$-0.747502\pi$
$41$	1.70574	−	2.95442i	0.266391	−	0.461403i	0.967927	+	0.251231i	$0.0808353\pi$
$42$		0			0
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	0.983747	−	0.179558i	$-0.0574668\pi$
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	−0.647376	+	0.762171i	$0.724133\pi$
$44$	1.01367	+	1.75573i	0.152817	+	0.264686i
$45$	0.701867	−	3.98048i	0.104628	−	0.593375i
$46$	3.93242	−	6.81115i	0.579803	−	1.00425i
$47$	4.67752	−	8.10170i	0.682286	−	1.18175i	−0.291995	−	0.956420i	$-0.594319\pi$
$47$	4.67752	−	8.10170i	0.682286	−	1.18175i	0.974281	−	0.225335i	$-0.0723475\pi$
$48$	0.0714517	−	0.0125989i	0.0103132	−	0.00181849i
$49$		0			0
$50$	−1.40033	+	2.42544i	−0.198037	+	0.343009i
$51$	0.798133	−	0.140732i	0.111761	−	0.0197065i
$52$	−4.13341			−0.573201
$53$	0.286989	−	0.497079i	0.0394210	−	0.0682791i	−0.845642	−	0.533751i	$-0.820782\pi$
$53$	0.286989	−	0.497079i	0.0394210	−	0.0682791i	0.885063	+	0.465472i	$0.154115\pi$
$54$			4.56942i			0.621819i
$55$	−2.22668			−0.300246
$56$		0			0
$57$	1.91147	−	5.25173i	0.253181	−	0.695609i
$58$	−5.51249			−0.723825
$59$	−5.19846	−	9.00400i	−0.676782	−	1.17222i	−0.975945	−	0.218019i	$-0.930041\pi$
$59$	−5.19846	−	9.00400i	−0.676782	−	1.17222i	0.299162	−	0.954202i	$-0.403293\pi$
$60$	0.979055	−	2.68993i	0.126396	−	0.347269i
$61$	3.81908	−	6.61484i	0.488983	−	0.846943i	−0.510937	−	0.859618i	$-0.670701\pi$
$61$	3.81908	−	6.61484i	0.488983	−	0.846943i	0.999920	+	0.0126752i	$0.00403474\pi$
$62$	8.12061			1.03132
$63$		0			0
$64$	5.04189			0.630236
$65$	2.26991	−	3.93161i	0.281548	−	0.487656i
$66$	2.47906	−	0.437124i	0.305151	−	0.0538063i
$67$	−0.298133	−	0.516382i	−0.0364228	−	0.0630861i	0.847239	−	0.531211i	$-0.178263\pi$
$67$	−0.298133	−	0.516382i	−0.0364228	−	0.0630861i	−0.883662	+	0.468125i	$0.844930\pi$
$68$	0.573978			0.0696051
$69$	9.95723	+	11.8666i	1.19871	+	1.42857i
$70$		0			0
$71$	−0.554378			−0.0657925			−0.0328963	−	0.999459i	$-0.510473\pi$
$71$	−0.554378			−0.0657925			−0.0328963	+	0.999459i	$0.510473\pi$
$72$	−1.47818	+	8.38316i	−0.174205	+	0.987965i
$73$	1.02481	−	1.77503i	0.119946	−	0.207752i	−0.799800	−	0.600266i	$-0.795061\pi$
$73$	1.02481	−	1.77503i	0.119946	−	0.207752i	0.919746	+	0.392514i	$0.128395\pi$
$74$	−8.12061			−0.944002
$75$	−3.54576	−	4.22567i	−0.409429	−	0.487939i
$76$	1.97906	−	3.42782i	0.227013	−	0.393198i
$77$		0			0
$78$	−1.75537	+	4.82283i	−0.198756	+	0.546078i
$79$	1.20187	−	2.08169i	0.135221	−	0.234209i	−0.790461	−	0.612512i	$-0.790159\pi$
$79$	1.20187	−	2.08169i	0.135221	−	0.234209i	0.925682	+	0.378303i	$0.123492\pi$
$80$	−0.0282185	+	0.0488759i	−0.00315492	+	0.00546449i
$81$	−8.45723	−	3.07818i	−0.939693	−	0.342020i
$82$	−1.50000	−	2.59808i	−0.165647	−	0.286910i
$83$	−7.52481	−	13.0334i	−0.825956	−	1.43060i	−0.901187	−	0.433431i	$-0.857303\pi$
$83$	−7.52481	−	13.0334i	−0.825956	−	1.43060i	0.0752309	−	0.997166i	$-0.476031\pi$
$84$		0			0
$85$	−0.315207	+	0.545955i	−0.0341891	+	0.0592172i
$86$	3.87939			0.418325
$87$	3.71348	−	10.2027i	0.398127	−	1.09384i
$88$	4.68954			0.499907
$89$	4.54323	+	7.86911i	0.481582	+	0.834124i	0.999777	−	0.0211385i	$-0.00672911\pi$
$89$	4.54323	+	7.86911i	0.481582	+	0.834124i	−0.518195	+	0.855263i	$0.673396\pi$
$90$	−2.72281	−	2.28471i	−0.287010	−	0.240830i
$91$		0			0
$92$	5.48545	+	9.50108i	0.571898	+	0.990556i
$93$	−5.47044	+	15.0299i	−0.567258	+	1.55853i
$94$	−4.11334	−	7.12452i	−0.424259	−	0.734838i
$95$	2.17365	+	3.76487i	0.223012	+	0.386267i
$96$	−3.34002	+	9.17664i	−0.340890	+	0.936587i
$97$	−0.949493	−	1.64457i	−0.0964064	−	0.166981i	0.813788	−	0.581161i	$-0.197402\pi$
$97$	−0.949493	−	1.64457i	−0.0964064	−	0.166981i	−0.910195	+	0.414181i	$0.864068\pi$
$98$		0			0
$99$	−0.860967	+	4.88279i	−0.0865304	+	0.490738i
$100$	−1.95336	−	3.38332i	−0.195336	−	0.338332i
$101$	1.70914			0.170066			0.0850329	−	0.996378i	$-0.472900\pi$
$101$	1.70914			0.170066			0.0850329	+	0.996378i	$0.472900\pi$
$102$	0.243756	−	0.669713i	0.0241354	−	0.0663115i
$103$	3.63816			0.358478			0.179239	−	0.983806i	$-0.442636\pi$
$103$	3.63816			0.358478			0.179239	+	0.983806i	$0.442636\pi$
$104$	−4.78059	+	8.28023i	−0.468776	+	0.811943i
$105$		0			0
$106$	−0.252374	−	0.437124i	−0.0245127	−	0.0424573i
$107$	−3.56418	−	6.17334i	−0.344562	−	0.596799i	0.640712	−	0.767781i	$-0.278639\pi$
$107$	−3.56418	−	6.17334i	−0.344562	−	0.596799i	−0.985274	+	0.170982i	$0.945306\pi$
$108$	−5.52007	−	3.18701i	−0.531169	−	0.306670i
$109$	−0.201867	+	0.349643i	−0.0193353	+	0.0334898i	−0.875531	−	0.483162i	$-0.839488\pi$
$109$	−0.201867	+	0.349643i	−0.0193353	+	0.0334898i	0.856196	+	0.516651i	$0.172822\pi$
$110$	−0.979055	+	1.69577i	−0.0933493	+	0.161686i
$111$	5.47044	−	15.0299i	0.519231	−	1.42658i
$112$		0			0
$113$	−7.18479	+	12.4444i	−0.675888	+	1.17067i	0.300320	+	0.953839i	$0.402907\pi$
$113$	−7.18479	+	12.4444i	−0.675888	+	1.17067i	−0.976208	+	0.216835i	$0.930427\pi$
$114$	−3.15910	−	3.76487i	−0.295877	−	0.352612i
$115$	−12.0496			−1.12363
$116$	3.84477	−	6.65934i	0.356978	−	0.618304i
$117$	−7.74376	−	6.49778i	−0.715910	−	0.600720i
$118$	−9.14290			−0.841672
$119$		0			0
$120$	−4.25624	−	5.07239i	−0.388540	−	0.463044i
$121$	−8.26857			−0.751688
$122$	−3.35844	−	5.81699i	−0.304059	−	0.526646i
$123$	5.81908	−	1.02606i	0.524689	−	0.0925168i
$124$	−5.66385	+	9.81007i	−0.508629	+	0.880971i
$125$	11.0273			0.986315
$126$		0			0
$127$	−20.7716			−1.84318			−0.921589	−	0.388167i	$-0.873108\pi$
$127$	−20.7716			−1.84318			−0.921589	+	0.388167i	$0.873108\pi$
$128$	−3.42127	+	5.92582i	−0.302401	+	0.523774i
$129$	−2.61334	+	7.18009i	−0.230092	+	0.632172i
$130$	−1.99613	−	3.45740i	−0.175072	−	0.303234i
$131$	7.16519			0.626026			0.313013	−	0.949749i	$-0.398662\pi$
$131$	7.16519			0.626026			0.313013	+	0.949749i	$0.398662\pi$
$132$	−1.20099	+	3.29969i	−0.104533	+	0.287201i
$133$		0			0
$134$	−0.524348			−0.0452968
$135$	6.06283	−	3.50038i	0.521806	−	0.301265i
$136$	0.663848	−	1.14982i	0.0569245	−	0.0985961i
$137$	2.56893			0.219478			0.109739	−	0.993960i	$-0.464998\pi$
$137$	2.56893			0.219478			0.109739	+	0.993960i	$0.464998\pi$
$138$	13.4153	−	2.36549i	1.14199	−	0.201364i
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	−0.966272	−	0.257523i	$-0.917094\pi$
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	0.706158	+	0.708055i	$0.250427\pi$
$140$		0			0
$141$	15.9572	−	2.81369i	1.34384	−	0.236956i
$142$	−0.243756	+	0.422197i	−0.0204555	+	0.0354300i
$143$	−2.78446	+	4.82283i	−0.232848	+	0.403305i
$144$	0.0962667	+	0.0807773i	0.00802222	+	0.00673144i
$145$	4.22281	+	7.31412i	0.350685	+	0.607405i
$146$	−0.901207	−	1.56094i	−0.0745844	−	0.129184i
$147$		0			0
$148$	5.66385	−	9.81007i	0.465565	−	0.806383i
$149$	0.431074			0.0353150			0.0176575	−	0.999844i	$-0.494379\pi$
$149$	0.431074			0.0353150			0.0176575	+	0.999844i	$0.494379\pi$
$150$	−4.77719	+	0.842347i	−0.390056	+	0.0687774i
$151$	−2.47060			−0.201055			−0.100527	−	0.994934i	$-0.532053\pi$
$151$	−2.47060			−0.201055			−0.100527	+	0.994934i	$0.532053\pi$
$152$	−4.57785	−	7.92907i	−0.371313	−	0.643132i
$153$	1.07532	+	0.902302i	0.0869346	+	0.0729468i
$154$		0			0
$155$	−6.22075	−	10.7747i	−0.499663	−	0.865441i
$156$	−4.60189	−	5.48432i	−0.368446	−	0.439097i
$157$	5.06670	+	8.77579i	0.404367	+	0.700384i	0.994248	−	0.107106i	$-0.0341585\pi$
$157$	5.06670	+	8.77579i	0.404367	+	0.700384i	−0.589881	+	0.807491i	$0.700825\pi$
$158$	−1.05690	−	1.83061i	−0.0840828	−	0.145636i
$159$	0.979055	−	0.172634i	0.0776441	−	0.0136908i
$160$	−3.79813	−	6.57856i	−0.300269	−	0.520081i
$161$		0			0
$162$	−6.06283	+	5.08732i	−0.476341	+	0.399698i
$163$	1.29813	+	2.24843i	0.101678	+	0.176111i	0.912376	−	0.409353i	$-0.134246\pi$
$163$	1.29813	+	2.24843i	0.101678	+	0.176111i	−0.810698	+	0.585464i	$0.800912\pi$
$164$	4.18479			0.326777
$165$	−2.47906	−	2.95442i	−0.192994	−	0.230002i
$166$	−13.2344			−1.02719
$167$	−11.5915	+	20.0771i	−0.896979	+	1.55361i	−0.0656422	+	0.997843i	$0.520910\pi$
$167$	−11.5915	+	20.0771i	−0.896979	+	1.55361i	−0.831337	+	0.555769i	$0.812424\pi$
$168$		0			0
$169$	0.822948	+	1.42539i	0.0633037	+	0.109645i
$170$	0.277189	+	0.480105i	0.0212594	+	0.0368224i
$171$	9.09627	−	3.31077i	0.695609	−	0.253181i
$172$	−2.70574	+	4.68647i	−0.206311	+	0.357340i
$173$	−2.37598	+	4.11532i	−0.180643	+	0.312882i	−0.942100	−	0.335333i	$-0.891151\pi$
$173$	−2.37598	+	4.11532i	−0.180643	+	0.312882i	0.761457	+	0.648215i	$0.224484\pi$
$174$	−6.13728	−	7.31412i	−0.465266	−	0.554482i
$175$		0			0
$176$	0.0346151	−	0.0599551i	0.00260921	−	0.00451929i
$177$	6.15910	−	16.9220i	0.462946	−	1.27193i
$178$	7.99050			0.598914
$179$	4.26604	−	7.38901i	0.318859	−	0.552280i	−0.661391	−	0.750041i	$-0.730034\pi$
$179$	4.26604	−	7.38901i	0.318859	−	0.552280i	0.980250	+	0.197761i	$0.0633670\pi$
$180$	4.65910	−	1.69577i	0.347269	−	0.126396i
$181$	17.2344			1.28102			0.640512	−	0.767948i	$-0.278722\pi$
$181$	17.2344			1.28102			0.640512	+	0.767948i	$0.278722\pi$
$182$		0			0
$183$	13.0287	−	2.29731i	0.963108	−	0.169822i
$184$	25.3773			1.87084
$185$	6.22075	+	10.7747i	0.457359	+	0.792169i
$186$	9.04101	+	10.7747i	0.662919	+	0.790036i
$187$	0.386659	−	0.669713i	0.0282753	−	0.0489743i
$188$	11.4757			0.836948
$189$		0			0
$190$	3.82295			0.277346
$191$	−6.45471	+	11.1799i	−0.467046	+	0.808948i	−0.999291	−	0.0376425i	$-0.988015\pi$
$191$	−6.45471	+	11.1799i	−0.467046	+	0.808948i	0.532245	+	0.846590i	$0.321349\pi$
$192$	5.61334	+	6.68972i	0.405108	+	0.482789i
$193$	0.319078	+	0.552659i	0.0229677	+	0.0397813i	0.877281	−	0.479977i	$-0.159355\pi$
$193$	0.319078	+	0.552659i	0.0229677	+	0.0397813i	−0.854313	+	0.519759i	$0.826022\pi$
$194$	−1.66994			−0.119895
$195$	7.74376	−	1.36543i	0.554542	−	0.0977807i
$196$		0			0
$197$	11.4456			0.815467			0.407733	−	0.913101i	$-0.366319\pi$
$197$	11.4456			0.815467			0.407733	+	0.913101i	$0.366319\pi$
$198$	3.34002	+	2.80261i	0.237365	+	0.199173i
$199$	−1.81908	+	3.15074i	−0.128951	+	0.223350i	−0.923270	−	0.384151i	$-0.874494\pi$
$199$	−1.81908	+	3.15074i	−0.128951	+	0.223350i	0.794319	+	0.607500i	$0.207828\pi$
$200$	−9.03684			−0.639001
$201$	0.353226	−	0.970481i	0.0249147	−	0.0684524i
$202$	0.751497	−	1.30163i	0.0528751	−	0.0915824i
$203$		0			0
$204$	0.639033	+	0.761570i	0.0447413	+	0.0533206i
$205$	−2.29813	+	3.98048i	−0.160509	+	0.278009i
$206$	1.59967	−	2.77071i	0.111454	−	0.193045i
$207$	−4.65910	+	26.4231i	−0.323830	+	1.83653i
$208$	0.0705744	+	0.122238i	0.00489345	+	0.00847571i
$209$	−2.66637	−	4.61830i	−0.184437	−	0.319454i
$210$		0			0
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	−0.948668	−	0.316273i	$-0.897569\pi$
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	0.748234	+	0.663435i	$0.230902\pi$
$212$	0.704088			0.0483570
$213$	−0.617211	−	0.735564i	−0.0422906	−	0.0504000i
$214$	−6.26857			−0.428511
$215$	−2.97178	−	5.14728i	−0.202674	−	0.351041i
$216$	−12.7687	+	7.37203i	−0.868802	+	0.501603i
$217$		0			0
$218$	0.177519	+	0.307471i	0.0120231	+	0.0208246i
$219$	3.49613	−	0.616462i	0.236247	−	0.0416566i
$220$	−1.36571	−	2.36549i	−0.0920765	−	0.159481i
$221$	0.788333	+	1.36543i	0.0530290	+	0.0918490i
$222$	−9.04101	−	10.7747i	−0.606793	−	0.723148i
$223$	3.54189	+	6.13473i	0.237182	+	0.410812i	0.959905	−	0.280327i	$-0.0904428\pi$
$223$	3.54189	+	6.13473i	0.237182	+	0.410812i	−0.722722	+	0.691139i	$0.757109\pi$
$224$		0			0
$225$	1.65910	−	9.40923i	0.110607	−	0.627282i
$226$	6.31820	+	10.9434i	0.420280	+	0.727947i
$227$	11.9436			0.792722			0.396361	−	0.918095i	$-0.370273\pi$
$227$	11.9436			0.792722			0.396361	+	0.918095i	$0.370273\pi$
$228$	6.75150	−	1.19047i	0.447129	−	0.0788409i
$229$	17.5526			1.15991			0.579955	−	0.814649i	$-0.303070\pi$
$229$	17.5526			1.15991			0.579955	+	0.814649i	$0.303070\pi$
$230$	−5.29813	+	9.17664i	−0.349349	+	0.605089i
$231$		0			0
$232$	−8.89352	−	15.4040i	−0.583888	−	1.01132i
$233$	−8.12701	−	14.0764i	−0.532418	−	0.922175i	−0.999284	−	0.0378470i	$-0.987950\pi$
$233$	−8.12701	−	14.0764i	−0.532418	−	0.922175i	0.466865	−	0.884328i	$-0.345383\pi$
$234$	−8.35339	+	3.04038i	−0.546078	+	0.198756i
$235$	−6.30200	+	10.9154i	−0.411097	+	0.712042i
$236$	6.37686	−	11.0450i	0.415098	−	0.718971i
$237$	4.10014	−	0.722965i	0.266333	−	0.0469616i
$238$		0			0
$239$	7.54963	−	13.0763i	0.488345	−	0.845838i	−0.511565	−	0.859244i	$-0.670934\pi$
$239$	7.54963	−	13.0763i	0.488345	−	0.845838i	0.999910	+	0.0134062i	$0.00426745\pi$
$240$	−0.0962667	+	0.0169744i	−0.00621399	+	0.00109569i
$241$	15.6382			1.00734			0.503671	−	0.863896i	$-0.331982\pi$
$241$	15.6382			1.00734			0.503671	+	0.863896i	$0.331982\pi$
$242$	−3.63563	+	6.29710i	−0.233707	+	0.404793i
$243$	−5.33157	−	14.6484i	−0.342020	−	0.939693i
$244$	9.36959			0.599826
$245$		0			0
$246$	1.77719	−	4.88279i	0.113309	−	0.311315i
$247$	10.8726			0.691806
$248$	13.1013	+	22.6922i	0.831935	+	1.44095i
$249$	8.91534	−	24.4947i	0.564987	−	1.55229i
$250$	4.84864	−	8.39809i	0.306655	−	0.531142i
$251$	−19.0651			−1.20338			−0.601690	−	0.798730i	$-0.705506\pi$
$251$	−19.0651			−1.20338			−0.601690	+	0.798730i	$0.705506\pi$
$252$		0			0
$253$	14.7811			0.929277
$254$	−9.13310	+	15.8190i	−0.573062	+	0.992572i
$255$	−1.07532	+	0.189608i	−0.0673393	+	0.0118737i
$256$	8.05051	+	13.9439i	0.503157	+	0.871493i
$257$	−26.5817			−1.65812			−0.829061	−	0.559158i	$-0.811124\pi$
$257$	−26.5817			−1.65812			−0.829061	+	0.559158i	$0.811124\pi$
$258$	4.31908	+	5.14728i	0.268894	+	0.320455i
$259$		0			0
$260$	5.56893			0.345370
$261$	17.6716	−	6.43193i	1.09384	−	0.398127i
$262$	3.15048	−	5.45680i	0.194637	−	0.337122i
$263$	−0.734118			−0.0452676			−0.0226338	−	0.999744i	$-0.507205\pi$
$263$	−0.734118			−0.0452676			−0.0226338	+	0.999744i	$0.507205\pi$
$264$	5.22106	+	6.22221i	0.321334	+	0.382951i
$265$	−0.386659	+	0.669713i	−0.0237523	+	0.0411402i
$266$		0			0
$267$	−5.38279	+	14.7891i	−0.329421	+	0.905078i
$268$	0.365715	−	0.633436i	0.0223396	−	0.0386933i
$269$	−10.4251	+	18.0569i	−0.635632	+	1.10095i	0.350749	+	0.936470i	$0.385927\pi$
$269$	−10.4251	+	18.0569i	−0.635632	+	1.10095i	−0.986381	+	0.164478i	$0.947406\pi$
$270$		−	6.15636i		−	0.374664i
$271$	3.47906	+	6.02590i	0.211338	+	0.366047i	0.952133	−	0.305683i	$-0.0988847\pi$
$271$	3.47906	+	6.02590i	0.211338	+	0.366047i	−0.740796	+	0.671730i	$0.765551\pi$
$272$	−0.00980018	−	0.0169744i	−0.000594223	−	0.00102922i
$273$		0			0
$274$	1.12954	−	1.95642i	0.0682379	−	0.118191i
$275$	−5.26352			−0.317402
$276$	−6.49912	+	17.8562i	−0.391201	+	1.07482i
$277$	17.8726			1.07386			0.536930	−	0.843627i	$-0.319584\pi$
$277$	17.8726			1.07386			0.536930	+	0.843627i	$0.319584\pi$
$278$	2.69681	+	4.67102i	0.161744	+	0.280149i
$279$	−26.0326	+	9.47508i	−1.55853	+	0.567258i
$280$		0			0
$281$	−11.1552	−	19.3214i	−0.665465	−	1.15262i	−0.979159	−	0.203095i	$-0.934900\pi$
$281$	−11.1552	−	19.3214i	−0.665465	−	1.15262i	0.313694	−	0.949524i	$-0.398433\pi$
$282$	4.87346	−	13.3897i	0.290210	−	0.797346i
$283$	−9.29726	−	16.1033i	−0.552665	−	0.957243i	−0.998081	−	0.0619196i	$-0.980278\pi$
$283$	−9.29726	−	16.1033i	−0.552665	−	0.957243i	0.445417	−	0.895323i	$-0.353056\pi$
$284$	−0.340022	−	0.588936i	−0.0201766	−	0.0349469i
$285$	−2.57532	+	7.07564i	−0.152549	+	0.419125i
$286$	2.44862	+	4.24113i	0.144790	+	0.250783i
$287$		0			0
$288$	−15.8944	+	5.78509i	−0.936587	+	0.340890i
$289$	8.39053	+	14.5328i	0.493561	+	0.854872i
$290$	7.42696			0.436126
$291$	1.12495	−	3.09078i	0.0659459	−	0.181185i
$292$	2.51424			0.147135
$293$	6.54576	−	11.3376i	0.382407	−	0.662349i	−0.608998	−	0.793171i	$-0.708428\pi$
$293$	6.54576	−	11.3376i	0.382407	−	0.662349i	0.991406	+	0.130822i	$0.0417618\pi$
$294$		0			0
$295$	7.00387	+	12.1311i	0.407781	+	0.706298i
$296$	−13.1013	−	22.6922i	−0.761499	−	1.31895i
$297$	−7.43717	+	4.29385i	−0.431548	+	0.249154i
$298$	0.189540	−	0.328293i	0.0109798	−	0.0190175i
$299$	−15.0680	+	26.0986i	−0.871408	+	1.50932i
$300$	2.31433	−	6.35857i	0.133618	−	0.367112i
$301$		0			0
$302$	−1.08630	+	1.88153i	−0.0625098	+	0.108270i
$303$	1.90286	+	2.26774i	0.109316	+	0.130278i
$304$	−0.135163			−0.00775211
$305$	−5.14543	+	8.91215i	−0.294626	+	0.510308i
$306$	1.15998	−	0.422197i	0.0663115	−	0.0241354i
$307$	−6.31046			−0.360157			−0.180078	−	0.983652i	$-0.557635\pi$
$307$	−6.31046			−0.360157			−0.180078	+	0.983652i	$0.557635\pi$
$308$		0			0
$309$	4.05051	+	4.82721i	0.230425	+	0.274610i
$310$	−10.9409			−0.621400
$311$	−4.76217	−	8.24833i	−0.270038	−	0.467720i	0.698833	−	0.715285i	$-0.253703\pi$
$311$	−4.76217	−	8.24833i	−0.270038	−	0.467720i	−0.968871	+	0.247565i	$0.920370\pi$
$312$	−16.3089	+	2.87569i	−0.923308	+	0.162804i
$313$	−8.81433	+	15.2669i	−0.498215	+	0.862934i	−0.999998	−	0.00205946i	$-0.999344\pi$
$313$	−8.81433	+	15.2669i	−0.498215	+	0.862934i	0.501782	+	0.864994i	$0.332678\pi$
$314$	8.91117			0.502886
$315$		0			0
$316$	2.94862			0.165873
$317$	−4.03849	+	6.99486i	−0.226824	+	0.392871i	−0.956865	−	0.290533i	$-0.906168\pi$
$317$	−4.03849	+	6.99486i	−0.226824	+	0.392871i	0.730041	+	0.683403i	$0.239501\pi$
$318$	0.299011	−	0.821525i	0.0167677	−	0.0460688i
$319$	−5.18004	−	8.97210i	−0.290027	−	0.502341i
$320$	−6.79292			−0.379736
$321$	4.22281	−	11.6021i	0.235694	−	0.647565i
$322$		0			0
$323$	−1.50980			−0.0840075
$324$	−1.91710	−	10.8724i	−0.106506	−	0.604023i
$325$	5.36571	−	9.29369i	0.297636	−	0.515521i
$326$	2.28312			0.126450
$327$	−0.688663	+	0.121430i	−0.0380831	+	0.00671509i
$328$	4.84002	−	8.38316i	0.267246	−	0.462883i
$329$		0			0
$330$	−3.34002	+	0.588936i	−0.183862	+	0.0324199i
$331$	−11.5248	+	19.9616i	−0.633461	+	1.09719i	0.353378	+	0.935481i	$0.385033\pi$
$331$	−11.5248	+	19.9616i	−0.633461	+	1.09719i	−0.986839	+	0.161706i	$0.948300\pi$
$332$	9.23055	−	15.9878i	0.506592	−	0.877444i
$333$	26.0326	−	9.47508i	1.42658	−	0.519231i
$334$	10.1934	+	17.6555i	0.557759	+	0.966066i
$335$	0.401674	+	0.695720i	0.0219458	+	0.0380112i
$336$		0			0
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	0.135161	+	0.990824i	$0.456845\pi$
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	−0.925659	+	0.378359i	$0.876489\pi$
$338$	1.44738			0.0787269
$339$	−24.5107	+	4.32190i	−1.33124	+	0.234734i
$340$	−0.773318			−0.0419391
$341$	7.63088	+	13.2171i	0.413235	+	0.715745i
$342$	1.47818	−	8.38316i	0.0799307	−	0.453310i
$343$		0			0
$344$	6.25877	+	10.8405i	0.337450	+	0.584481i
$345$	−13.4153	−	15.9878i	−0.722258	−	0.860753i
$346$	2.08940	+	3.61895i	0.112327	+	0.194556i
$347$	−6.47313	−	11.2118i	−0.347496	−	0.601880i	0.638308	−	0.769781i	$-0.279635\pi$
$347$	−6.47313	−	11.2118i	−0.347496	−	0.601880i	−0.985804	+	0.167901i	$0.946301\pi$
$348$	13.1163	−	2.31276i	0.703109	−	0.123977i
$349$	0.731429	+	1.26687i	0.0391525	+	0.0678141i	0.884938	−	0.465710i	$-0.154201\pi$
$349$	0.731429	+	1.26687i	0.0391525	+	0.0678141i	−0.845785	+	0.533524i	$0.820868\pi$
$350$		0			0
$351$		−	17.5089i		−	0.934555i
$352$	4.65910	+	8.06980i	0.248331	+	0.430122i
$353$	−14.3327			−0.762855			−0.381428	−	0.924399i	$-0.624567\pi$
$353$	−14.3327			−0.762855			−0.381428	+	0.924399i	$0.624567\pi$
$354$	−10.1792	−	12.1311i	−0.541017	−	0.644759i
$355$	0.746911			0.0396419
$356$	−5.57310	+	9.65289i	−0.295374	+	0.511602i
$357$		0			0
$358$	−3.75150	−	6.49778i	−0.198273	−	0.343418i
$359$	10.4684	+	18.1318i	0.552500	+	0.956958i	0.998093	+	0.0617224i	$0.0196594\pi$
$359$	10.4684	+	18.1318i	0.552500	+	0.956958i	−0.445593	+	0.895235i	$0.647007\pi$
$360$	1.99154	−	11.2946i	0.104964	−	0.595278i
$361$	4.29426	−	7.43788i	0.226014	−	0.391467i
$362$	7.57785	−	13.1252i	0.398283	−	0.689846i
$363$	−9.20574	−	10.9710i	−0.483176	−	0.575827i
$364$		0			0
$365$	−1.38073	+	2.39149i	−0.0722707	+	0.125176i
$366$	3.97906	−	10.9324i	0.207989	−	0.571444i
$367$	12.0574			0.629390			0.314695	−	0.949193i	$-0.398098\pi$
$367$	12.0574			0.629390			0.314695	+	0.949193i	$0.398098\pi$
$368$	0.187319	−	0.324446i	0.00976466	−	0.0169129i
$369$	7.84002	+	6.57856i	0.408135	+	0.342466i
$370$	10.9409			0.568789
$371$		0			0
$372$	−19.3221	+	3.40700i	−1.00180	+	0.176645i
$373$	−0.781059			−0.0404417			−0.0202209	−	0.999796i	$-0.506437\pi$
$373$	−0.781059			−0.0404417			−0.0202209	+	0.999796i	$0.506437\pi$
$374$	−0.340022	−	0.588936i	−0.0175821	−	0.0304532i
$375$	12.2772	+	14.6314i	0.633991	+	0.755561i
$376$	13.2724	−	22.9885i	0.684474	−	1.18554i
$377$	21.1225			1.08786
$378$		0			0
$379$	−6.92396			−0.355660			−0.177830	−	0.984061i	$-0.556908\pi$
$379$	−6.92396			−0.355660			−0.177830	+	0.984061i	$0.556908\pi$
$380$	−2.66637	+	4.61830i	−0.136782	+	0.236914i
$381$	−23.1258	−	27.5603i	−1.18477	−	1.41196i
$382$	5.67617	+	9.83142i	0.290418	+	0.503019i
$383$	−7.73236			−0.395105			−0.197553	−	0.980292i	$-0.563299\pi$
$383$	−7.73236			−0.395105			−0.197553	+	0.980292i	$0.563299\pi$
$384$	−11.6716	+	2.05802i	−0.595613	+	0.105023i
$385$		0			0
$386$	0.561185			0.0285636
$387$	−12.4363	+	4.52644i	−0.632172	+	0.230092i
$388$	1.16473	−	2.01736i	0.0591300	−	0.102416i
$389$	5.39961			0.273771			0.136886	−	0.990587i	$-0.456291\pi$
$389$	5.39961			0.273771			0.136886	+	0.990587i	$0.456291\pi$
$390$	2.36500	−	6.49778i	0.119756	−	0.329028i
$391$	2.09240	−	3.62414i	0.105817	−	0.183280i
$392$		0			0
$393$	7.97730	+	9.50698i	0.402402	+	0.479564i
$394$	5.03256	−	8.71664i	0.253536	−	0.439138i
$395$	−1.61927	+	2.80466i	−0.0814743	+	0.141118i
$396$	−5.71523	+	2.08017i	−0.287201	+	0.104533i
$397$	−14.6172	−	25.3178i	−0.733617	−	1.27066i	−0.955328	−	0.295549i	$-0.904497\pi$
$397$	−14.6172	−	25.3178i	−0.733617	−	1.27066i	0.221711	−	0.975112i	$-0.428836\pi$
$398$	1.59967	+	2.77071i	0.0801842	+	0.138883i
$399$		0			0
$400$	−0.0667040	+	0.115535i	−0.00333520	+	0.00577674i
$401$	−27.3979			−1.36818			−0.684092	−	0.729396i	$-0.739801\pi$
$401$	−27.3979			−1.36818			−0.684092	+	0.729396i	$0.739801\pi$
$402$	−0.583778	−	0.695720i	−0.0291162	−	0.0346993i
$403$	−31.1162			−1.55001
$404$	1.04829	+	1.81568i	0.0521542	+	0.0903337i
$405$	11.3944	+	4.14722i	0.566192	+	0.206077i
$406$		0			0
$407$	−7.63088	−	13.2171i	−0.378249	−	0.655146i
$408$	2.26470	−	0.399328i	0.112119	−	0.0197697i
$409$	−4.51249	−	7.81586i	−0.223128	−	0.386469i	0.732628	−	0.680629i	$-0.238294\pi$
$409$	−4.51249	−	7.81586i	−0.223128	−	0.386469i	−0.955756	+	0.294160i	$0.904960\pi$
$410$	2.02094	+	3.50038i	0.0998073	+	0.172871i
$411$	2.86009	+	3.40852i	0.141078	+	0.168130i
$412$	2.23143	+	3.86495i	0.109935	+	0.190412i
$413$		0			0
$414$	18.0744	+	15.1663i	0.888310	+	0.745381i
$415$	10.1382	+	17.5598i	0.497662	+	0.861977i
$416$	−18.9982			−0.931466
$417$	−10.4620	+	1.84473i	−0.512325	+	0.0903368i
$418$	−4.68954			−0.229373
$419$	0.0876485	−	0.151812i	0.00428191	−	0.00741649i	−0.863877	−	0.503704i	$-0.831970\pi$
$419$	0.0876485	−	0.151812i	0.00428191	−	0.00741649i	0.868158	+	0.496287i	$0.165304\pi$
$420$		0			0
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	0.992514	+	0.122130i	$0.0389724\pi$
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	−0.390490	+	0.920607i	$0.627694\pi$
$422$	2.56031	+	4.43458i	0.124634	+	0.215872i
$423$	21.4991	+	18.0399i	1.04532	+	0.877130i
$424$	0.814330	−	1.41046i	0.0395474	−	0.0684980i
$425$	−0.745100	+	1.29055i	−0.0361427	+	0.0626009i
$426$	−0.831566	+	0.146628i	−0.0402895	+	0.00710413i
$427$		0			0
$428$	4.37211	−	7.57272i	0.211334	−	0.366041i
$429$	−9.49912	+	1.67495i	−0.458622	+	0.0808674i
$430$	−5.22668			−0.252053
$431$	14.6596	−	25.3911i	0.706126	−	1.22305i	−0.260157	−	0.965566i	$-0.583774\pi$
$431$	14.6596	−	25.3911i	0.706126	−	1.22305i	0.966283	−	0.257481i	$-0.0828924\pi$
$432$			0.217662i			0.0104723i
$433$	−19.6554			−0.944578			−0.472289	−	0.881444i	$-0.656572\pi$
$433$	−19.6554			−0.944578			−0.472289	+	0.881444i	$0.656572\pi$
$434$		0			0
$435$	−5.00316	+	13.7461i	−0.239883	+	0.659073i
$436$	−0.495252			−0.0237183
$437$	−14.4290	−	24.9918i	−0.690233	−	1.19552i
$438$	1.06774	−	2.93360i	0.0510188	−	0.140173i
$439$	−10.9650	+	18.9919i	−0.523330	+	0.906434i	0.476302	+	0.879282i	$0.341977\pi$
$439$	−10.9650	+	18.9919i	−0.523330	+	0.906434i	−0.999631	+	0.0271516i	$0.991356\pi$
$440$	−6.31820			−0.301208
$441$		0			0
$442$	1.38650			0.0659489
$443$	9.35504	−	16.2034i	0.444471	−	0.769847i	−0.553544	−	0.832820i	$-0.686725\pi$
$443$	9.35504	−	16.2034i	0.444471	−	0.769847i	0.998015	+	0.0629732i	$0.0200583\pi$
$444$	19.3221	−	3.40700i	0.916985	−	0.161689i
$445$	−6.12108	−	10.6020i	−0.290167	−	0.502584i
$446$	6.22937			0.294969
$447$	0.479933	+	0.571962i	0.0227000	+	0.0270529i
$448$		0			0
$449$	6.68004			0.315251			0.157625	−	0.987499i	$-0.449616\pi$
$449$	6.68004			0.315251			0.157625	+	0.987499i	$0.449616\pi$
$450$	−6.43629	−	5.40069i	−0.303410	−	0.254591i
$451$	2.81908	−	4.88279i	0.132745	−	0.229921i
$452$	−17.6269			−0.829100
$453$	−2.75062	−	3.27806i	−0.129235	−	0.154017i
$454$	5.25150	−	9.09586i	0.246465	−	0.426890i
$455$		0			0
$456$	5.42380	−	14.9018i	0.253993	−	0.697839i
$457$	9.71436	−	16.8258i	0.454418	−	0.787076i	−0.544236	−	0.838932i	$-0.683180\pi$
$457$	9.71436	−	16.8258i	0.454418	−	0.787076i	0.998655	+	0.0518563i	$0.0165138\pi$
$458$	7.71776	−	13.3676i	0.360627	−	0.624625i
$459$			2.43134i			0.113485i
$460$	−7.39053	−	12.8008i	−0.344585	−	0.596839i
$461$	−0.482926	−	0.836452i	−0.0224921	−	0.0389575i	0.854560	−	0.519352i	$-0.173827\pi$
$461$	−0.482926	−	0.836452i	−0.0224921	−	0.0389575i	−0.877052	+	0.480395i	$0.840493\pi$
$462$		0			0
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	−0.860802	−	0.508941i	$-0.830037\pi$
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	0.871156	+	0.491006i	$0.163371\pi$
$464$	−0.262585			−0.0121902
$465$	7.37030	−	20.2497i	0.341789	−	0.939059i
$466$	−14.2935			−0.662136
$467$	−17.1074	−	29.6309i	−0.791637	−	1.37115i	−0.924953	−	0.380081i	$-0.875896\pi$
$467$	−17.1074	−	29.6309i	−0.791637	−	1.37115i	0.133317	−	0.991074i	$-0.457437\pi$
$468$	2.15328	−	12.2118i	0.0995352	−	0.564492i
$469$		0			0
$470$	5.54189	+	9.59883i	0.255628	+	0.442761i
$471$	−6.00299	+	16.4931i	−0.276603	+	0.759961i
$472$	−14.7506	−	25.5488i	−0.678952	−	1.17598i
$473$	3.64543	+	6.31407i	0.167617	+	0.290321i
$474$	1.25221	−	3.44042i	0.0575160	−	0.158024i
$475$	5.13816	+	8.89955i	0.235755	+	0.408339i
$476$		0			0
$477$	1.31908	+	1.10684i	0.0603964	+	0.0506786i
$478$	−6.63903	−	11.4991i	−0.303662	−	0.525959i
$479$	21.7929			0.995744			0.497872	−	0.867251i	$-0.334115\pi$
$479$	21.7929			0.995744			0.497872	+	0.867251i	$0.334115\pi$
$480$	4.50000	−	12.3636i	0.205396	−	0.564321i
$481$	31.1162			1.41878
$482$	6.87598	−	11.9095i	0.313192	−	0.542465i
$483$		0			0
$484$	−5.07145	−	8.78401i	−0.230521	−	0.399273i
$485$	1.27925	+	2.21572i	0.0580877	+	0.100611i
$486$	−13.5000	−	2.38041i	−0.612372	−	0.107978i
$487$	−9.69640	+	16.7947i	−0.439386	+	0.761039i	−0.997642	−	0.0686297i	$-0.978137\pi$
$487$	−9.69640	+	16.7947i	−0.439386	+	0.761039i	0.558256	+	0.829669i	$0.311471\pi$
$488$	10.8366	−	18.7696i	0.490551	−	0.849659i
$489$	−1.53802	+	4.22567i	−0.0695516	+	0.191091i
$490$		0			0
$491$	−13.0783	+	22.6523i	−0.590216	+	1.02228i	0.403987	+	0.914765i	$0.367624\pi$
$491$	−13.0783	+	22.6523i	−0.590216	+	1.02228i	−0.994203	+	0.107519i	$0.965709\pi$
$492$	4.65910	+	5.55250i	0.210048	+	0.250326i
$493$	−2.93313			−0.132102
$494$	4.78059	−	8.28023i	0.215089	−	0.372545i
$495$	1.15998	−	6.57856i	0.0521371	−	0.295684i
$496$	0.386821			0.0173688
$497$		0			0
$498$	−14.7344	−	17.5598i	−0.660265	−	0.786873i
$499$	−14.3013			−0.640214			−0.320107	−	0.947381i	$-0.603719\pi$
$499$	−14.3013			−0.640214			−0.320107	+	0.947381i	$0.603719\pi$
$500$	6.76352	+	11.7148i	0.302474	+	0.523900i
$501$	−39.5442	+	6.97270i	−1.76670	+	0.311517i
$502$	−8.38279	+	14.5194i	−0.374142	+	0.648033i
$503$	−18.7033			−0.833937			−0.416969	−	0.908921i	$-0.636908\pi$
$503$	−18.7033			−0.833937			−0.416969	+	0.908921i	$0.636908\pi$
$504$		0			0
$505$	−2.30272			−0.102470
$506$	6.49912	−	11.2568i	0.288921	−	0.500426i
$507$	−0.975023	+	2.67885i	−0.0433023	+	0.118972i
$508$	−12.7400	−	22.0664i	−0.565248	−	0.979039i
$509$	25.6091			1.13510			0.567551	−	0.823338i	$-0.307891\pi$
$509$	25.6091			1.13510			0.567551	+	0.823338i	$0.307891\pi$
$510$	−0.328411	+	0.902302i	−0.0145423	+	0.0399546i
$511$		0			0
$512$	0.473897			0.0209435
$513$	14.5201	+	8.38316i	0.641077	+	0.370126i
$514$	−11.6878	+	20.2438i	−0.515526	+	0.892917i
$515$	−4.90167			−0.215994
$516$	−9.23055	+	1.62760i	−0.406352	+	0.0716509i
$517$	7.73055	−	13.3897i	0.339989	−	0.588879i
$518$		0			0
$519$	−8.10560	+	1.42924i	−0.355796	+	0.0627365i
$520$	6.44087	−	11.1559i	0.282451	−	0.489220i
$521$	−10.6061	+	18.3702i	−0.464660	+	0.804815i	−0.999186	−	0.0403370i	$-0.987157\pi$
$521$	−10.6061	+	18.3702i	−0.464660	+	0.804815i	0.534526	+	0.845152i	$0.320490\pi$
$522$	2.87170	−	16.2862i	0.125691	−	0.712829i
$523$	10.4029	+	18.0183i	0.454885	+	0.787884i	0.998682	−	0.0513330i	$-0.0163470\pi$
$523$	10.4029	+	18.0183i	0.454885	+	0.787884i	−0.543796	+	0.839217i	$0.683014\pi$
$524$	4.39470	+	7.61185i	0.191984	+	0.332525i
$525$		0			0
$526$	−0.322786	+	0.559082i	−0.0140741	+	0.0243771i
$527$	4.32089			0.188221
$528$	0.118089	−	0.0208222i	0.00513914	−	0.000906170i
$529$	56.9873			2.47771
$530$	0.340022	+	0.588936i	0.0147696	+	0.0255817i
$531$	29.3097	−	10.6679i	1.27193	−	0.462946i
$532$		0			0
$533$	5.74763	+	9.95518i	0.248957	+	0.431207i
$534$	8.89615	+	10.6020i	0.384974	+	0.458794i
$535$	4.80200	+	8.31731i	0.207609	+	0.359589i
$536$	−0.845952	−	1.46523i	−0.0365396	−	0.0632884i
$537$	14.5535	−	2.56617i	0.628030	−	0.110739i
$538$	9.16772	+	15.8790i	0.395248	+	0.684590i
$539$		0			0
$540$	7.43717	+	4.29385i	0.320045	+	0.184778i
$541$	−13.3648	−	23.1486i	−0.574599	−	0.995235i	−0.996085	−	0.0884001i	$-0.971825\pi$
$541$	−13.3648	−	23.1486i	−0.574599	−	0.995235i	0.421486	−	0.906835i	$-0.361509\pi$
$542$	6.11886			0.262828
$543$	19.1878	+	22.8671i	0.823427	+	0.981322i
$544$	2.63816			0.113110
$545$	0.271974	−	0.471073i	0.0116501	−	0.0201786i
$546$		0			0
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	−0.928446	−	0.371467i	$-0.878855\pi$
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	0.142523	−	0.989792i	$-0.454479\pi$
$548$	1.57563	+	2.72907i	0.0673074	+	0.116580i
$549$	17.5535	+	14.7291i	0.749165	+	0.628624i
$550$	−2.31433	+	4.00854i	−0.0986834	+	0.170925i
$551$	−10.1133	+	17.5168i	−0.430843	+	0.746242i
$552$	28.2536	+	33.6713i	1.20255	+	1.43315i
$553$		0			0
$554$	7.85844	−	13.6112i	0.333873	−	0.578285i
$555$	−7.37030	+	20.2497i	−0.312852	+	0.859553i
$556$	−7.52374			−0.319078
$557$	−16.1694	+	28.0062i	−0.685118	+	1.18666i	0.288282	+	0.957546i	$0.406916\pi$
$557$	−16.1694	+	28.0062i	−0.685118	+	1.18666i	−0.973400	+	0.229114i	$0.926417\pi$
$558$	−4.23039	+	23.9917i	−0.179087	+	1.01565i
$559$	−14.8648			−0.628716
$560$		0			0
$561$	1.31908	−	0.232589i	0.0556915	−	0.00981992i
$562$	−19.6195			−0.827598
$563$	−8.87093	−	15.3649i	−0.373865	−	0.647553i	0.616291	−	0.787518i	$-0.288634\pi$
$563$	−8.87093	−	15.3649i	−0.373865	−	0.647553i	−0.990156	+	0.139965i	$0.955301\pi$
$564$	12.7763	+	15.2262i	0.537980	+	0.641139i
$565$	9.68004	−	16.7663i	0.407243	−	0.705365i
$566$	−16.3517			−0.687315
$567$		0			0
$568$	−1.57304			−0.0660035
$569$	13.3007	−	23.0374i	0.557593	−	0.965779i	−0.440104	−	0.897947i	$-0.645058\pi$
$569$	13.3007	−	23.0374i	0.557593	−	0.965779i	0.997697	−	0.0678320i	$-0.0216082\pi$
$570$	4.25624	+	5.07239i	0.178274	+	0.212459i
$571$	5.00862	+	8.67518i	0.209604	+	0.363045i	0.951590	−	0.307371i	$-0.0994491\pi$
$571$	5.00862	+	8.67518i	0.209604	+	0.363045i	−0.741986	+	0.670416i	$0.766116\pi$
$572$	−6.83130			−0.285631
$573$	−22.0201	+	3.88273i	−0.919902	+	0.162203i
$574$		0			0
$575$	−28.4834			−1.18784
$576$	−2.62654	+	14.8959i	−0.109439	+	0.620661i
$577$	−16.4572	+	28.5048i	−0.685124	+	1.18667i	0.288274	+	0.957548i	$0.406918\pi$
$577$	−16.4572	+	28.5048i	−0.685124	+	1.18667i	−0.973398	+	0.229121i	$0.926415\pi$
$578$	14.7570			0.613811
$579$	−0.378041	+	1.03866i	−0.0157109	+	0.0431652i
$580$	−5.18004	+	8.97210i	−0.215090	+	0.372546i
$581$		0			0
$582$	−1.85921	−	2.21572i	−0.0770668	−	0.0918447i
$583$	0.474308	−	0.821525i	0.0196438	−	0.0340241i
$584$	2.90791	−	5.03665i	0.120330	−	0.208418i
$585$	10.4331	+	8.75444i	0.431357	+	0.361951i
$586$	−5.75624	−	9.97011i	−0.237788	−	0.411861i
$587$	−7.53643	−	13.0535i	−0.311062	−	0.538774i	0.667531	−	0.744582i	$-0.267351\pi$
$587$	−7.53643	−	13.0535i	−0.311062	−	0.538774i	−0.978592	+	0.205808i	$0.934018\pi$
$588$		0			0
$589$	14.8983	−	25.8046i	0.613873	−	1.06326i
$590$	12.3182			0.507132
$591$	12.7429	+	15.1864i	0.524172	+	0.624684i
$592$	−0.386821			−0.0158983
$593$	20.5005	+	35.5079i	0.841853	+	1.45813i	0.888326	+	0.459213i	$0.151869\pi$
$593$	20.5005	+	35.5079i	0.841853	+	1.45813i	−0.0464729	+	0.998920i	$0.514798\pi$
$594$			7.55190i			0.309858i
$595$		0			0
$596$	0.264396	+	0.457947i	0.0108301	+	0.0187582i
$597$	−6.20574	+	1.09424i	−0.253984	+	0.0447842i
$598$	13.2506	+	22.9507i	0.541858	+	0.938526i
$599$	−3.03684	−	5.25996i	−0.124082	−	0.214916i	0.797292	−	0.603594i	$-0.206265\pi$
$599$	−3.03684	−	5.25996i	−0.124082	−	0.214916i	−0.921374	+	0.388678i	$0.872932\pi$
$600$	−10.0611	−	11.9903i	−0.410742	−	0.489503i
$601$	−7.06758	−	12.2414i	−0.288293	−	0.499338i	0.685110	−	0.728440i	$-0.259754\pi$
$601$	−7.06758	−	12.2414i	−0.288293	−	0.499338i	−0.973402	+	0.229102i	$0.926421\pi$
$602$		0			0
$603$	1.68092	−	0.611806i	0.0684524	−	0.0249147i
$604$	−1.51532	−	2.62461i	−0.0616575	−	0.106794i
$605$	11.1402			0.452914
$606$	2.56371	−	0.452051i	0.104144	−	0.0183633i
$607$	−46.0898			−1.87073			−0.935363	−	0.353689i	$-0.884927\pi$
$607$	−46.0898			−1.87073			−0.935363	+	0.353689i	$0.884927\pi$
$608$	9.09627	−	15.7552i	0.368902	−	0.638958i
$609$		0			0
$610$	4.52481	+	7.83721i	0.183204	+	0.317319i
$611$	15.7613	+	27.2994i	0.637634	+	1.10441i
$612$	−0.299011	+	1.69577i	−0.0120868	+	0.0685476i
$613$	13.2469	−	22.9443i	0.535038	−	0.926712i	−0.464124	−	0.885770i	$-0.653631\pi$
$613$	13.2469	−	22.9443i	0.535038	−	0.926712i	0.999162	−	0.0409421i	$-0.0130359\pi$
$614$	−2.77466	+	4.80586i	−0.111976	+	0.193949i
$615$	−7.84002	+	1.38241i	−0.316140	+	0.0557440i
$616$		0			0
$617$	1.12495	−	1.94847i	0.0452889	−	0.0784426i	−0.842492	−	0.538708i	$-0.818913\pi$
$617$	1.12495	−	1.94847i	0.0452889	−	0.0784426i	0.887781	+	0.460266i	$0.152246\pi$
$618$	5.45723	−	0.962258i	0.219522	−	0.0387077i
$619$	−6.19078			−0.248828			−0.124414	−	0.992230i	$-0.539705\pi$
$619$	−6.19078			−0.248828			−0.124414	+	0.992230i	$0.539705\pi$
$620$	7.63088	−	13.2171i	0.306464	−	0.530811i
$621$	−40.2460	+	23.2361i	−1.61502	+	0.932431i
$622$	−8.37557			−0.335830
$623$		0			0
$624$	−0.0836160	+	0.229733i	−0.00334732	+	0.00919668i
$625$	1.06687			0.0426746
$626$	7.75119	+	13.4255i	0.309800	+	0.536589i
$627$	3.15910	−	8.67956i	0.126162	−	0.346628i
$628$	−6.21523	+	10.7651i	−0.248015	+	0.429574i
$629$	−4.32089			−0.172285
$630$		0			0
$631$	26.1661			1.04166			0.520829	−	0.853661i	$-0.325623\pi$
$631$	26.1661			1.04166			0.520829	+	0.853661i	$0.325623\pi$
$632$	3.41029	−	5.90680i	0.135654	−	0.234960i
$633$	−9.93242	+	1.75135i	−0.394778	+	0.0696100i
$634$	3.55138	+	6.15118i	0.141043	+	0.244295i
$635$	27.9855			1.11057
$636$	0.783890	+	0.934204i	0.0310833	+	0.0370436i
$637$		0			0
$638$	−9.11051			−0.360689
$639$	0.288800	−	1.63787i	0.0114248	−	0.0647930i
$640$	4.60947	−	7.98384i	0.182205	−	0.315589i
$641$	4.88888			0.193099			0.0965496	−	0.995328i	$-0.469219\pi$
$641$	4.88888			0.193099			0.0965496	+	0.995328i	$0.469219\pi$
$642$	−6.97906	−	8.31731i	−0.275441	−	0.328258i
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	0.126242	+	0.992000i	$0.459709\pi$
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	−0.922218	+	0.386671i	$0.873625\pi$
$644$		0			0
$645$	3.52094	−	9.67372i	0.138637	−	0.380902i
$646$	−0.663848	+	1.14982i	−0.0261188	+	0.0452390i
$647$	−1.14038	+	1.97519i	−0.0448329	+	0.0776528i	−0.887571	−	0.460671i	$-0.847609\pi$
$647$	−1.14038	+	1.97519i	−0.0448329	+	0.0776528i	0.842738	+	0.538324i	$0.180942\pi$
$648$	−23.9974	−	8.73433i	−0.942706	−	0.343117i
$649$	−8.59152	−	14.8809i	−0.337247	−	0.584128i
$650$	−4.71853	−	8.17273i	−0.185076	−	0.320561i
$651$		0			0
$652$	−1.59240	+	2.75811i	−0.0623631	+	0.108016i
$653$	23.4793			0.918815			0.459407	−	0.888226i	$-0.348062\pi$
$653$	23.4793			0.918815			0.459407	+	0.888226i	$0.348062\pi$
$654$	−0.210323	+	0.577857i	−0.00822427	+	0.0225960i
$655$	−9.65364			−0.377199
$656$	−0.0714517	−	0.123758i	−0.00278972	−	0.00483194i
$657$	4.71032	+	3.95243i	0.183767	+	0.154199i
$658$		0			0
$659$	23.9812	+	41.5366i	0.934174	+	1.61804i	0.776101	+	0.630609i	$0.217195\pi$
$659$	23.9812	+	41.5366i	0.934174	+	1.61804i	0.158073	+	0.987427i	$0.449472\pi$
$660$	1.61809	−	4.44566i	0.0629840	−	0.173047i
$661$	14.6545	+	25.3824i	0.569995	+	0.987260i	0.996566	+	0.0828055i	$0.0263880\pi$
$661$	14.6545	+	25.3824i	0.569995	+	0.987260i	−0.426571	+	0.904454i	$0.640279\pi$
$662$	10.1348	+	17.5539i	0.393898	+	0.682252i
$663$	−0.934011	+	2.56617i	−0.0362740	+	0.0996620i
$664$	−21.3516	−	36.9821i	−0.828604	−	1.43518i
$665$		0			0
$666$	4.23039	−	23.9917i	0.163924	−	0.929661i
$667$	−28.0317	−	48.5523i	−1.08539	−	1.87995i
$668$	−28.4382			−1.10031
$669$	−4.19640	+	11.5295i	−0.162242	+	0.445757i
$670$	0.706452			0.0272926
$671$	6.31180	−	10.9324i	0.243664	−	0.422039i
$672$		0			0
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	−0.999965	−	0.00838731i	$-0.997330\pi$
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	0.492719	−	0.870189i	$-0.336003\pi$
$674$	12.7613	+	22.1032i	0.491547	+	0.851384i
$675$	14.3316	−	8.27433i	0.551622	−	0.318479i
$676$	−1.00950	+	1.74850i	−0.0388267	+	0.0672499i
$677$	17.9454	−	31.0823i	0.689697	−	1.19459i	−0.282239	−	0.959344i	$-0.591077\pi$
$677$	17.9454	−	31.0823i	0.689697	−	1.19459i	0.971936	−	0.235246i	$-0.0755895\pi$
$678$	−7.48576	+	20.5669i	−0.287489	+	0.789869i
$679$		0			0
$680$	−0.894400	+	1.54915i	−0.0342987	+	0.0594070i
$681$	13.2973	+	15.8471i	0.509552	+	0.607260i
$682$	13.4210			0.513915
$683$	−17.5321	+	30.3665i	−0.670847	+	1.16194i	0.306818	+	0.951768i	$0.400736\pi$
$683$	−17.5321	+	30.3665i	−0.670847	+	1.16194i	−0.977664	+	0.210172i	$0.932597\pi$
$684$	9.09627	+	7.63267i	0.347804	+	0.291843i
$685$	−3.46110			−0.132242
$686$		0			0
$687$	19.5421	+	23.2893i	0.745576	+	0.888543i
$688$	0.184793			0.00704515
$689$	0.967034	+	1.67495i	0.0368411	+	0.0638106i
$690$	−18.0744	+	3.18701i	−0.688082	+	0.121327i
$691$	1.03343	−	1.78996i	0.0393136	−	0.0680932i	−0.845699	−	0.533660i	$-0.820816\pi$
$691$	1.03343	−	1.78996i	0.0393136	−	0.0680932i	0.885013	+	0.465567i	$0.154150\pi$
$692$	−5.82915			−0.221591
$693$		0			0
$694$	−11.3847			−0.432159
$695$	4.13176	−	7.15642i	0.156727	−	0.271458i
$696$	10.5370	−	28.9501i	0.399403	−	1.09735i
$697$	−0.798133	−	1.38241i	−0.0302315	−	0.0523624i
$698$	1.28642			0.0486916
$699$	9.62882	−	26.4550i	0.364196	−	1.00062i
$700$		0			0
$701$	−7.36009			−0.277987			−0.138993	−	0.990293i	$-0.544387\pi$
$701$	−7.36009			−0.277987			−0.138993	+	0.990293i	$0.544387\pi$
$702$	−13.3342	−	7.69852i	−0.503268	−	0.290562i
$703$	−14.8983	+	25.8046i	−0.561899	+	0.973237i
$704$	8.33275			0.314052
$705$	−21.4991	+	3.79088i	−0.809704	+	0.142773i
$706$	−6.30200	+	10.9154i	−0.237179	+	0.410806i
$707$		0			0
$708$	21.7545	−	3.83590i	0.817584	−	0.144162i
$709$	−4.55438	+	7.88841i	−0.171043	+	0.296256i	−0.938785	−	0.344504i	$-0.888047\pi$
$709$	−4.55438	+	7.88841i	−0.171043	+	0.296256i	0.767742	+	0.640760i	$0.221380\pi$
$710$	0.328411	−	0.568825i	0.0123251	−	0.0213476i
$711$	5.52410	+	4.63527i	0.207170	+	0.173836i
$712$	12.8914	+	22.3286i	0.483126	+	0.836799i
$713$	41.2943	+	71.5239i	1.54648	+	2.67859i
$714$		0			0
$715$	3.75150	−	6.49778i	0.140298	−	0.243003i
$716$	10.4662			0.391139
$717$	25.7554	−	4.54137i	0.961852	−	0.169600i
$718$	18.4115			0.687110
$719$	−12.9768	−	22.4765i	−0.483954	−	0.838233i	0.515876	−	0.856663i	$-0.327467\pi$
$719$	−12.9768	−	22.4765i	−0.483954	−	0.838233i	−0.999830	+	0.0184300i	$0.994133\pi$
$720$	−0.129700	−	0.108831i	−0.00483362	−	0.00405589i
$721$		0			0
$722$	−3.77631	−	6.54076i	−0.140540	−	0.243422i
$723$	17.4106	+	20.7491i	0.647507	+	0.771669i
$724$	10.5706	+	18.3088i	0.392852	+	0.680440i
$725$	9.98205	+	17.2894i	0.370724	+	0.642113i
$726$	−12.4029	+	2.18696i	−0.460313	+	0.0811656i
$727$	−5.08007	−	8.79894i	−0.188409	−	0.326335i	0.756311	−	0.654213i	$-0.227000\pi$
$727$	−5.08007	−	8.79894i	−0.188409	−	0.326335i	−0.944720	+	0.327878i	$0.893667\pi$
$728$		0			0
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	1.21419	+	2.10304i	0.0449393	+	0.0778372i
$731$	2.06418			0.0763464
$732$	10.4315	+	12.4318i	0.385561	+	0.459494i
$733$	−40.6614			−1.50186			−0.750931	−	0.660381i	$-0.770395\pi$
$733$	−40.6614			−1.50186			−0.750931	+	0.660381i	$0.770395\pi$
$734$	5.30154	−	9.18253i	0.195683	−	0.338933i
$735$		0			0
$736$	25.2126	+	43.6695i	0.929349	+	1.60968i
$737$	−0.492726	−	0.853427i	−0.0181498	−	0.0314364i
$738$	8.45723	−	3.07818i	0.311315	−	0.113309i
$739$	12.6809	−	21.9640i	0.466475	−	0.807959i	−0.532791	−	0.846247i	$-0.678857\pi$
$739$	12.6809	−	21.9640i	0.466475	−	0.807959i	0.999267	+	0.0382877i	$0.0121903\pi$
$740$	−7.63088	+	13.2171i	−0.280517	+	0.485869i
$741$	12.1049	+	14.4260i	0.444684	+	0.529954i
$742$		0			0
$743$	11.2221	−	19.4372i	0.411699	−	0.713083i	−0.583377	−	0.812202i	$-0.698269\pi$
$743$	11.2221	−	19.4372i	0.411699	−	0.713083i	0.995076	+	0.0991184i	$0.0316023\pi$
$744$	−15.5223	+	42.6473i	−0.569077	+	1.56353i
$745$	−0.580785			−0.0212783
$746$	−0.343426	+	0.594831i	−0.0125737	+	0.0217783i
$747$	42.4261	−	15.4418i	1.55229	−	0.564987i
$748$	0.948615			0.0346848
$749$		0			0
$750$	16.5410	−	2.91663i	0.603992	−	0.106500i
$751$	24.2172			0.883698			0.441849	−	0.897090i	$-0.354323\pi$
$751$	24.2172			0.883698			0.441849	+	0.897090i	$0.354323\pi$
$752$	−0.195937	−	0.339373i	−0.00714508	−	0.0123756i
$753$	−21.2260	−	25.2961i	−0.773517	−	0.921842i
$754$	9.28740	−	16.0862i	0.338227	−	0.585827i
$755$	3.32863			0.121141
$756$		0			0
$757$	9.11793			0.331397			0.165698	−	0.986176i	$-0.447012\pi$
$757$	9.11793			0.331397			0.165698	+	0.986176i	$0.447012\pi$
$758$	−3.04442	+	5.27308i	−0.110578	+	0.191527i
$759$	16.4564	+	19.6119i	0.597328	+	0.711868i
$760$	6.16772	+	10.6828i	0.223727	+	0.387506i
$761$	18.2722			0.662366			0.331183	−	0.943566i	$-0.392552\pi$
$761$	18.2722			0.662366			0.331183	+	0.943566i	$0.392552\pi$
$762$	−31.1573	+	5.49388i	−1.12871	+	0.199022i
$763$		0			0
$764$	−15.8357			−0.572917
$765$	−1.44878	−	1.21567i	−0.0523807	−	0.0439526i
$766$	−3.39986	+	5.88874i	−0.122842	+	0.212769i
$767$	35.0333			1.26498
$768$	−9.53818	+	26.2059i	−0.344179	+	0.945625i
$769$	9.26470	−	16.0469i	0.334094	−	0.578667i	−0.649217	−	0.760604i	$-0.724903\pi$
$769$	9.26470	−	16.0469i	0.334094	−	0.578667i	0.983310	+	0.181936i	$0.0582365\pi$
$770$		0			0
$771$	−29.5945	−	35.2694i	−1.06582	−	1.27020i
$772$	−0.391407	+	0.677937i	−0.0140870	+	0.0243995i
$773$	−1.48040	+	2.56413i	−0.0532463	+	0.0922253i	−0.891420	−	0.453178i	$-0.850290\pi$
$773$	−1.48040	+	2.56413i	−0.0532463	+	0.0922253i	0.838174	+	0.545403i	$0.183624\pi$
$774$	−2.02094	+	11.4613i	−0.0726414	+	0.411970i
$775$	−14.7049	−	25.4696i	−0.528214	−	0.914894i
$776$	−2.69418	−	4.66646i	−0.0967155	−	0.167516i
$777$		0			0
$778$	2.37417	−	4.11218i	0.0851181	−	0.147429i
$779$	−11.0077			−0.394393
$780$	6.20011	+	7.38901i	0.222000	+	0.264569i
$781$	−0.916222			−0.0327850
$782$	−1.84002	−	3.18701i	−0.0657991	−	0.113967i
$783$	28.2086	+	16.2862i	1.00809	+	0.582022i
$784$		0			0
$785$	−6.82635	−	11.8236i	−0.243643	−	0.422002i
$786$	10.7478	−	1.89513i	0.383361	−	0.0675969i
$787$	−16.7010	−	28.9270i	−0.595326	−	1.03113i	−0.993501	−	0.113825i	$-0.963690\pi$
$787$	−16.7010	−	28.9270i	−0.595326	−	1.03113i	0.398175	−	0.917310i	$-0.369644\pi$
$788$	7.02007	+	12.1591i	0.250080	+	0.433150i
$789$	−0.817323	−	0.974048i	−0.0290975	−	0.0346770i
$790$	1.42396	+	2.46638i	0.0506623	+	0.0877497i
$791$		0			0
$792$	−2.44299	+	13.8549i	−0.0868079	+	0.492312i
$793$	12.8687	+	22.2893i	0.456981	+	0.791515i
$794$	−25.7083			−0.912354
$795$	−1.31908	+	0.232589i	−0.0467829	+	0.00824908i
$796$	−4.46286			−0.158182
$797$	24.6755	−	42.7391i	0.874050	−	1.51390i	0.0162779	−	0.999868i	$-0.494818\pi$
$797$	24.6755	−	42.7391i	0.874050	−	1.51390i	0.857772	−	0.514031i	$-0.171848\pi$
$798$		0			0
$799$	−2.18866	−	3.79088i	−0.0774293	−	0.134112i
$800$	−8.97818	−	15.5507i	−0.317427	−	0.549799i
$801$	−25.6155	+	9.32326i	−0.905078	+	0.329421i
$802$	−12.0466	+	20.8654i	−0.425382	+	0.736782i
$803$	1.69372	−	2.93360i	0.0597699	−	0.103525i
$804$	1.24763	−	0.219990i	0.0440004	−	0.00775845i
$805$		0			0
$806$	−13.6816	+	23.6971i	−0.481912	+	0.834696i
$807$	−35.5651	+	6.27109i	−1.25195	+	0.220753i
$808$	4.84968			0.170611
$809$	−9.91400	+	17.1716i	−0.348558	+	0.603720i	−0.985993	−	0.166784i	$-0.946662\pi$
$809$	−9.91400	+	17.1716i	−0.348558	+	0.603720i	0.637436	+	0.770503i	$0.279995\pi$
$810$	8.16843	−	6.85413i	0.287010	−	0.240830i
$811$	23.8557			0.837686			0.418843	−	0.908059i	$-0.362436\pi$
$811$	23.8557			0.837686			0.418843	+	0.908059i	$0.362436\pi$
$812$		0			0
$813$	−4.12196	+	11.3250i	−0.144563	+	0.397185i
$814$	−13.4210			−0.470405
$815$	−1.74897	−	3.02931i	−0.0612638	−	0.106112i
$816$	0.0116112	−	0.0319015i	0.000406473	−	0.00111677i
$817$	7.11721	−	12.3274i	0.249000	−	0.431280i
$818$	−7.93643			−0.277491
$819$		0			0
$820$	−5.63816			−0.196893
$821$	25.4714	−	44.1177i	0.888957	−	1.53972i	0.0478469	−	0.998855i	$-0.484764\pi$
$821$	25.4714	−	44.1177i	0.888957	−	1.53972i	0.841110	−	0.540864i	$-0.181903\pi$
$822$	3.85339	−	0.679456i	0.134402	−	0.0236988i
$823$	−6.80747	−	11.7909i	−0.237293	−	0.411004i	0.722643	−	0.691221i	$-0.242927\pi$
$823$	−6.80747	−	11.7909i	−0.237293	−	0.411004i	−0.959937	+	0.280217i	$0.909594\pi$
$824$	10.3233			0.359628
$825$	−5.86009	−	6.98378i	−0.204022	−	0.243144i
$826$		0			0
$827$	36.2158			1.25935			0.629673	−	0.776861i	$-0.283189\pi$
$827$	36.2158			1.25935			0.629673	+	0.776861i	$0.283189\pi$
$828$	−30.9278	+	11.2568i	−1.07482	+	0.391201i
$829$	12.6630	−	21.9329i	0.439803	−	0.761761i	−0.557871	−	0.829928i	$-0.688382\pi$
$829$	12.6630	−	21.9329i	0.439803	−	0.761761i	0.997674	+	0.0681664i	$0.0217149\pi$
$830$	17.8307			0.618912
$831$	19.8983	+	23.7138i	0.690263	+	0.822624i
$832$	−8.49454	+	14.7130i	−0.294495	+	0.510080i
$833$		0			0
$834$	−3.19517	+	8.77864i	−0.110640	+	0.303980i
$835$	15.6172	−	27.0498i	0.540456	−	0.936097i
$836$	3.27079	−	5.66518i	0.113123	−	0.195934i
$837$	−41.5549	−	23.9917i	−1.43635	−	0.829276i
$838$	−0.0770768	−	0.133501i	−0.00266257	−	0.00461171i
$839$	4.35710	+	7.54671i	0.150424	+	0.260541i	0.931383	−	0.364040i	$-0.118603\pi$
$839$	4.35710	+	7.54671i	0.150424	+	0.260541i	−0.780960	+	0.624582i	$0.785270\pi$
$840$		0			0
$841$	−5.14749	+	8.91571i	−0.177500	+	0.307438i
$842$	21.7252			0.748701
$843$	13.2166	−	36.3124i	0.455205	−	1.25067i
$844$	−7.14290			−0.245869
$845$	−1.10876	−	1.92042i	−0.0381423	−	0.0660645i
$846$	23.1917	−	8.44107i	0.797346	−	0.290210i
$847$		0			0
$848$	−0.0120217	−	0.0208222i	−0.000412827	−	0.000715037i
$849$	11.0153	−	30.2643i	0.378045	−	1.03867i
$850$	0.655230	+	1.13489i	0.0224742	+	0.0389265i
$851$	−41.2943	−	71.5239i	−1.41555	−	2.45181i
$852$	0.402856	−	1.10684i	0.0138016	−	0.0379196i
$853$	−5.99067	−	10.3761i	−0.205117	−	0.355272i	0.745053	−	0.667005i	$-0.232424\pi$
$853$	−5.99067	−	10.3761i	−0.205117	−	0.355272i	−0.950170	+	0.311733i	$0.899091\pi$
$854$		0			0
$855$	−12.2554	+	4.46059i	−0.419125	+	0.152549i
$856$	−10.1133	−	17.5168i	−0.345667	−	0.598713i
$857$	−6.50030			−0.222046			−0.111023	−	0.993818i	$-0.535413\pi$
$857$	−6.50030			−0.222046			−0.111023	+	0.993818i	$0.535413\pi$
$858$	−2.90110	+	7.97071i	−0.0990420	+	0.272116i
$859$	53.5526			1.82719			0.913596	−	0.406623i	$-0.133294\pi$
$859$	53.5526			1.82719			0.913596	+	0.406623i	$0.133294\pi$
$860$	3.64543	−	6.31407i	0.124308	−	0.215308i
$861$		0			0
$862$	−12.8914	−	22.3286i	−0.439083	−	0.760514i
$863$	−1.84982	−	3.20399i	−0.0629687	−	0.109065i	0.832822	−	0.553540i	$-0.186723\pi$
$863$	−1.84982	−	3.20399i	−0.0629687	−	0.109065i	−0.895791	+	0.444475i	$0.853390\pi$
$864$	−25.3717	−	14.6484i	−0.863163	−	0.498347i
$865$	3.20115	−	5.54456i	0.108842	−	0.188521i
$866$	−8.64233	+	14.9690i	−0.293678	+	0.508666i
$867$	−9.94104	+	27.3128i	−0.337615	+	0.927590i
$868$		0			0
$869$	1.98633	−	3.44042i	0.0673816	−	0.116708i
$870$	8.26873	+	9.85429i	0.280336	+	0.334092i
$871$	2.00917			0.0680782
$872$	−0.572796	+	0.992112i	−0.0193973	+	0.0335971i
$873$	5.35339	−	1.94847i	0.181185	−	0.0659459i
$874$	−25.3773			−0.858401
$875$		0			0
$876$	2.79921	+	3.33597i	0.0945765	+	0.112712i
$877$	−11.7888			−0.398079			−0.199040	−	0.979991i	$-0.563782\pi$
$877$	−11.7888			−0.398079			−0.199040	+	0.979991i	$0.563782\pi$
$878$	9.64244	+	16.7012i	0.325416	+	0.563638i
$879$	22.3307	−	3.93750i	0.753195	−	0.132809i
$880$	−0.0466368	+	0.0807773i	−0.00157213	+	0.00272300i
$881$	−49.4858			−1.66722			−0.833609	−	0.552355i	$-0.813729\pi$
$881$	−49.4858			−1.66722			−0.833609	+	0.552355i	$0.813729\pi$
$882$		0			0
$883$	−21.5357			−0.724734			−0.362367	−	0.932035i	$-0.618031\pi$
$883$	−21.5357			−0.724734			−0.362367	+	0.932035i	$0.618031\pi$
$884$	−0.967034	+	1.67495i	−0.0325249	+	0.0563347i
$885$	−8.29813	+	22.7989i	−0.278939	+	0.766378i
$886$	−8.22668	−	14.2490i	−0.276381	−	0.478706i
$887$	−11.8848			−0.399051			−0.199526	−	0.979893i	$-0.563940\pi$
$887$	−11.8848			−0.399051			−0.199526	+	0.979893i	$0.563940\pi$
$888$	15.5223	−	42.6473i	0.520896	−	1.43115i
$889$		0			0
$890$	−10.7656			−0.360863
$891$	−13.9773	−	5.08732i	−0.468257	−	0.170432i
$892$	−4.34477	+	7.52536i	−0.145474	+	0.251968i
$893$	−30.1857			−1.01013
$894$	0.646612	−	0.114015i	0.0216259	−	0.00381324i
$895$	−5.74763	+	9.95518i	−0.192122	+	0.332765i
$896$		0			0
$897$	−51.4043	+	9.06396i	−1.71634	+	0.302637i
$898$	2.93717	−	5.08732i	0.0980145	−	0.169766i
$899$	28.9433	−	50.1313i	0.965314	−	1.67197i
$900$	11.0134	−	4.00854i	0.367112	−	0.133618i
$901$	−0.134285	−	0.232589i	−0.00447369	−	0.00774866i
$902$	−2.47906	−	4.29385i	−0.0825435	−	0.142970i
$903$		0			0
$904$	−20.3868	+	35.3110i	−0.678056	+	1.17443i
$905$	−23.2199			−0.771855
$906$	−3.70590	+	0.653450i	−0.123120	+	0.0217094i
$907$	−26.0215			−0.864029			−0.432014	−	0.901867i	$-0.642197\pi$
$907$	−26.0215			−0.864029			−0.432014	+	0.901867i	$0.642197\pi$
$908$	7.32547	+	12.6881i	0.243104	+	0.421069i
$909$	−0.890367	+	5.04952i	−0.0295316	+	0.167482i
$910$		0			0
$911$	2.01636	+	3.49244i	0.0668050	+	0.115710i	0.897493	−	0.441028i	$-0.145386\pi$
$911$	2.01636	+	3.49244i	0.0668050	+	0.115710i	−0.830688	+	0.556738i	$0.812053\pi$
$912$	−0.150482	−	0.179338i	−0.00498296	−	0.00593846i
$913$	−12.4363	−	21.5403i	−0.411581	−	0.712879i
$914$	−8.54266	−	14.7963i	−0.282566	−	0.489419i
$915$	−17.5535	+	3.09516i	−0.580301	+	0.102323i
$916$	10.7657	+	18.6468i	0.355710	+	0.616108i
$917$		0			0
$918$	1.85163	+	1.06904i	0.0611130	+	0.0352836i
$919$	−13.7135	−	23.7524i	−0.452366	−	0.783521i	0.546167	−	0.837677i	$-0.316087\pi$
$919$	−13.7135	−	23.7524i	−0.452366	−	0.783521i	−0.998532	+	0.0541559i	$0.982753\pi$
$920$	−34.1908			−1.12724
$921$	−7.02569	−	8.37289i	−0.231504	−	0.275896i
$922$	−0.849356			−0.0279720
$923$	0.934011	−	1.61775i	0.0307434	−	0.0532491i
$924$		0			0
$925$	14.7049	+	25.4696i	0.483493	+	0.837434i
$926$	−0.195937	−	0.339373i	−0.00643889	−	0.0111525i
$927$	−1.89528	+	10.7487i	−0.0622491	+	0.353032i
$928$	17.6716	−	30.6081i	0.580098	−	1.00476i
$929$	3.83837	−	6.64826i	0.125933	−	0.218122i	−0.796164	−	0.605081i	$-0.793141\pi$
$929$	3.83837	−	6.64826i	0.125933	−	0.218122i	0.922097	+	0.386958i	$0.126474\pi$
$930$	−12.1809	−	14.5167i	−0.399428	−	0.476020i
$931$		0			0
$932$	9.96926	−	17.2673i	0.326554	−	0.565608i
$933$	5.64219	−	15.5018i	0.184717	−	0.507506i
$934$	−30.0880			−0.984510
$935$	−0.520945	+	0.902302i	−0.0170367	+	0.0295084i
$936$	−21.9729	−	18.4374i	−0.718206	−	0.602646i
$937$	2.02465			0.0661425			0.0330713	−	0.999453i	$-0.489471\pi$
$937$	2.02465			0.0661425			0.0330713	+	0.999453i	$0.489471\pi$
$938$		0			0
$939$	−30.0699	+	5.30213i	−0.981293	+	0.173028i
$940$	−15.4611			−0.504286
$941$	−3.06964	−	5.31677i	−0.100067	−	0.173322i	0.811645	−	0.584151i	$-0.198573\pi$
$941$	−3.06964	−	5.31677i	−0.100067	−	0.173322i	−0.911712	+	0.410829i	$0.865239\pi$
$942$	9.92117	+	11.8236i	0.323249	+	0.385233i
$943$	15.2554	−	26.4231i	0.496783	−	0.860454i
$944$	−0.435518			−0.0141749
$945$		0			0
$946$	6.41147			0.208455
$947$	−2.78224	+	4.81898i	−0.0904107	+	0.156596i	−0.907684	−	0.419654i	$-0.862151\pi$
$947$	−2.78224	+	4.81898i	−0.0904107	+	0.156596i	0.817273	+	0.576250i	$0.195485\pi$
$948$	3.28281	+	3.91231i	0.106621	+	0.127066i
$949$	3.45320	+	5.98112i	0.112096	+	0.194155i
$950$	9.03684			0.293194
$951$	−13.7772	+	2.42929i	−0.446756	+	0.0787751i
$952$		0			0
$953$	−8.72018			−0.282474			−0.141237	−	0.989976i	$-0.545108\pi$
$953$	−8.72018			−0.282474			−0.141237	+	0.989976i	$0.545108\pi$
$954$	1.42292	−	0.517902i	0.0460688	−	0.0167677i
$955$	8.69640	−	15.0626i	0.281409	−	0.487415i
$956$	18.5220			0.599044
$957$	6.13728	−	16.8620i	0.198390	−	0.545072i
$958$	9.58219	−	16.5968i	0.309586	−	0.536219i
$959$		0			0
$960$	−7.56283	−	9.01303i	−0.244089	−	0.290894i
$961$	−27.1373	+	47.0031i	−0.875396	+	1.51623i
$962$	13.6816	−	23.6971i	0.441111	−	0.764027i
$963$	20.0954	−	7.31412i	0.647565	−	0.235694i
$964$	9.59152	+	16.6130i	0.308922	+	0.535069i
$965$	−0.429892	−	0.744596i	−0.0138387	−	0.0239694i
$966$		0			0
$967$	28.8849	−	50.0301i	0.928876	−	1.60886i	0.143670	−	0.989626i	$-0.454110\pi$
$967$	28.8849	−	50.0301i	0.928876	−	1.60886i	0.785206	−	0.619235i	$-0.212557\pi$
$968$	−23.4620			−0.754098
$969$	−1.68092	−	2.00324i	−0.0539990	−	0.0643535i
$970$	2.24990			0.0722401
$971$	−15.3596	−	26.6036i	−0.492914	−	0.853752i	0.507053	−	0.861915i	$-0.330735\pi$
$971$	−15.3596	−	26.6036i	−0.492914	−	0.853752i	−0.999967	+	0.00816326i	$0.997402\pi$
$972$	12.2914	−	14.6484i	0.394248	−	0.469846i
$973$		0			0
$974$	8.52687	+	14.7690i	0.273219	+	0.473229i
$975$	18.3050	−	3.22766i	0.586229	−	0.103368i
$976$	−0.159978	−	0.277089i	−0.00512076	−	0.00886941i
$977$	−5.15002	−	8.92009i	−0.164764	−	0.285379i	0.771808	−	0.635856i	$-0.219353\pi$
$977$	−5.15002	−	8.92009i	−0.164764	−	0.285379i	−0.936571	+	0.350477i	$0.886019\pi$
$978$	2.54189	+	3.02931i	0.0812806	+	0.0968665i
$979$	7.50862	+	13.0053i	0.239976	+	0.415651i
$980$		0			0
$981$	−0.927833	−	0.778544i	−0.0296234	−	0.0248570i
$982$	11.5009	+	19.9201i	0.367008	+	0.635676i
$983$	−13.6963			−0.436846			−0.218423	−	0.975854i	$-0.570091\pi$
$983$	−13.6963			−0.436846			−0.218423	+	0.975854i	$0.570091\pi$
$984$	16.5116	−	2.91144i	0.526371	−	0.0928134i
$985$	−15.4206			−0.491343
$986$	−1.28968	+	2.23379i	−0.0410717	+	0.0711383i
$987$		0			0
$988$	6.66860	+	11.5503i	0.212156	+	0.367465i
$989$	19.7271	+	34.1684i	0.627287	+	1.08649i
$990$	−4.50000	−	3.77595i	−0.143019	−	0.120008i
$991$	−28.9907	+	50.2133i	−0.920919	+	1.59508i	−0.122922	+	0.992416i	$0.539227\pi$
$991$	−28.9907	+	50.2133i	−0.920919	+	1.59508i	−0.797997	+	0.602662i	$0.794107\pi$
$992$	−26.0326	+	45.0897i	−0.826534	+	1.43160i
$993$	−39.3166	+	6.93258i	−1.24767	+	0.219999i
$994$		0			0
$995$	2.45084	−	4.24497i	0.0776968	−	0.134575i
$996$	31.4898	−	5.55250i	0.997792	−	0.175938i
$997$	−16.2175			−0.513614			−0.256807	−	0.966463i	$-0.582670\pi$
$997$	−16.2175			−0.513614			−0.256807	+	0.966463i	$0.582670\pi$
$998$	−6.28817	+	10.8914i	−0.199049	+	0.344762i
$999$	41.5549	+	23.9917i	1.31474	+	0.759065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.g.b.67.3		6
3.2	odd	2		1323.2.g.e.361.1		6
7.2	even	3		441.2.h.e.373.1		6
7.3	odd	6		63.2.f.a.22.3	✓	6
7.4	even	3		441.2.f.c.148.3		6
7.5	odd	6		441.2.h.d.373.1		6
7.6	odd	2		441.2.g.c.67.3		6
9.2	odd	6		1323.2.h.b.802.3		6
9.7	even	3		441.2.h.e.214.1		6
21.2	odd	6		1323.2.h.b.226.3		6
21.5	even	6		1323.2.h.c.226.3		6
21.11	odd	6		1323.2.f.d.442.1		6
21.17	even	6		189.2.f.b.64.1		6
21.20	even	2		1323.2.g.d.361.1		6
28.3	even	6		1008.2.r.h.337.2		6
63.2	odd	6		1323.2.g.e.667.1		6
63.4	even	3		3969.2.a.q.1.1		3
63.11	odd	6		1323.2.f.d.883.1		6
63.16	even	3	inner	441.2.g.b.79.3		6
63.20	even	6		1323.2.h.c.802.3		6
63.25	even	3		441.2.f.c.295.3		6
63.31	odd	6		567.2.a.h.1.1		3
63.32	odd	6		3969.2.a.l.1.3		3
63.34	odd	6		441.2.h.d.214.1		6
63.38	even	6		189.2.f.b.127.1		6
63.47	even	6		1323.2.g.d.667.1		6
63.52	odd	6		63.2.f.a.43.3	yes	6
63.59	even	6		567.2.a.c.1.3		3
63.61	odd	6		441.2.g.c.79.3		6
84.59	odd	6		3024.2.r.k.1009.2		6
252.31	even	6		9072.2.a.ca.1.2		3
252.59	odd	6		9072.2.a.bs.1.2		3
252.115	even	6		1008.2.r.h.673.2		6
252.227	odd	6		3024.2.r.k.2017.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.3	✓	6	7.3	odd	6
63.2.f.a.43.3	yes	6	63.52	odd	6
189.2.f.b.64.1		6	21.17	even	6
189.2.f.b.127.1		6	63.38	even	6
441.2.f.c.148.3		6	7.4	even	3
441.2.f.c.295.3		6	63.25	even	3
441.2.g.b.67.3		6	1.1	even	1	trivial
441.2.g.b.79.3		6	63.16	even	3	inner
441.2.g.c.67.3		6	7.6	odd	2
441.2.g.c.79.3		6	63.61	odd	6
441.2.h.d.214.1		6	63.34	odd	6
441.2.h.d.373.1		6	7.5	odd	6
441.2.h.e.214.1		6	9.7	even	3
441.2.h.e.373.1		6	7.2	even	3
567.2.a.c.1.3		3	63.59	even	6
567.2.a.h.1.1		3	63.31	odd	6
1008.2.r.h.337.2		6	28.3	even	6
1008.2.r.h.673.2		6	252.115	even	6
1323.2.f.d.442.1		6	21.11	odd	6
1323.2.f.d.883.1		6	63.11	odd	6
1323.2.g.d.361.1		6	21.20	even	2
1323.2.g.d.667.1		6	63.47	even	6
1323.2.g.e.361.1		6	3.2	odd	2
1323.2.g.e.667.1		6	63.2	odd	6
1323.2.h.b.226.3		6	21.2	odd	6
1323.2.h.b.802.3		6	9.2	odd	6
1323.2.h.c.226.3		6	21.5	even	6
1323.2.h.c.802.3		6	63.20	even	6
3024.2.r.k.1009.2		6	84.59	odd	6
3024.2.r.k.2017.2		6	252.227	odd	6
3969.2.a.l.1.3		3	63.32	odd	6
3969.2.a.q.1.1		3	63.4	even	3
9072.2.a.bs.1.2		3	252.59	odd	6
9072.2.a.ca.1.2		3	252.31	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.439693 - 0.761570i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} -1.34730 q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})\)	\(q+(0.439693 - 0.761570i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} -1.34730 q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +(-0.592396 + 1.02606i) q^{10} +1.65270 q^{11} +(-0.726682 + 1.99654i) q^{12} +(-1.68479 + 2.91815i) q^{13} +(-1.50000 - 1.78763i) q^{15} +(0.0209445 - 0.0362770i) q^{16} +(0.233956 - 0.405223i) q^{17} +(2.02094 + 1.69577i) q^{18} +(-1.61334 - 2.79439i) q^{19} +(-0.826352 - 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +8.94356 q^{23} +(3.15910 + 3.76487i) q^{24} -3.18479 q^{25} +(1.48158 + 2.56617i) q^{26} +(-4.50000 + 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(-2.02094 + 0.356347i) q^{30} +(4.61721 + 7.99724i) q^{31} +(2.81908 + 4.88279i) q^{32} +(1.84002 + 2.19285i) q^{33} +(-0.205737 - 0.356347i) q^{34} +(-3.45811 + 1.25865i) q^{36} +(-4.61721 - 7.99724i) q^{37} -2.83750 q^{38} +(-5.74763 + 1.01346i) q^{39} -3.82295 q^{40} +(1.70574 - 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +(1.01367 + 1.75573i) q^{44} +(0.701867 - 3.98048i) q^{45} +(3.93242 - 6.81115i) q^{46} +(4.67752 - 8.10170i) q^{47} +(0.0714517 - 0.0125989i) q^{48} +(-1.40033 + 2.42544i) q^{50} +(0.798133 - 0.140732i) q^{51} -4.13341 q^{52} +(0.286989 - 0.497079i) q^{53} +4.56942i q^{54} -2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} -5.51249 q^{58} +(-5.19846 - 9.00400i) q^{59} +(0.979055 - 2.68993i) q^{60} +(3.81908 - 6.61484i) q^{61} +8.12061 q^{62} +5.04189 q^{64} +(2.26991 - 3.93161i) q^{65} +(2.47906 - 0.437124i) q^{66} +(-0.298133 - 0.516382i) q^{67} +0.573978 q^{68} +(9.95723 + 11.8666i) q^{69} -0.554378 q^{71} +(-1.47818 + 8.38316i) q^{72} +(1.02481 - 1.77503i) q^{73} -8.12061 q^{74} +(-3.54576 - 4.22567i) q^{75} +(1.97906 - 3.42782i) q^{76} +(-1.75537 + 4.82283i) q^{78} +(1.20187 - 2.08169i) q^{79} +(-0.0282185 + 0.0488759i) q^{80} +(-8.45723 - 3.07818i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-7.52481 - 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +3.87939 q^{86} +(3.71348 - 10.2027i) q^{87} +4.68954 q^{88} +(4.54323 + 7.86911i) q^{89} +(-2.72281 - 2.28471i) q^{90} +(5.48545 + 9.50108i) q^{92} +(-5.47044 + 15.0299i) q^{93} +(-4.11334 - 7.12452i) q^{94} +(2.17365 + 3.76487i) q^{95} +(-3.34002 + 9.17664i) q^{96} +(-0.949493 - 1.64457i) q^{97} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 9 * q^6 + 12 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 9 q^{6} + 12 q^{8} + 12 q^{11} + 9 q^{12} - 3 q^{13} - 9 q^{15} - 3 q^{16} + 6 q^{17} + 9 q^{18} - 3 q^{19} - 6 q^{20} - 9 q^{22} + 24 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 27 q^{27} - 9 q^{29} - 9 q^{30} - 3 q^{31} - 9 q^{33} + 9 q^{34} - 27 q^{36} + 3 q^{37} - 12 q^{38} - 18 q^{39} + 18 q^{40} + 3 q^{43} - 15 q^{44} + 18 q^{45} + 3 q^{47} + 6 q^{50} - 9 q^{51} + 42 q^{52} - 6 q^{53} - 9 q^{57} - 18 q^{58} - 3 q^{59} + 9 q^{60} + 6 q^{61} + 60 q^{62} + 24 q^{64} - 15 q^{65} + 18 q^{66} + 12 q^{67} - 12 q^{68} + 9 q^{69} + 18 q^{71} + 45 q^{72} - 21 q^{73} - 60 q^{74} + 9 q^{75} + 15 q^{76} + 54 q^{78} + 21 q^{79} - 15 q^{80} - 9 q^{82} - 18 q^{83} - 9 q^{85} + 12 q^{86} - 36 q^{87} + 54 q^{88} + 12 q^{89} - 27 q^{90} - 3 q^{92} - 27 q^{93} - 18 q^{94} + 12 q^{95} - 3 q^{97} + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 9 * q^6 + 12 * q^8 + 12 * q^11 + 9 * q^12 - 3 * q^13 - 9 * q^15 - 3 * q^16 + 6 * q^17 + 9 * q^18 - 3 * q^19 - 6 * q^20 - 9 * q^22 + 24 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 27 * q^27 - 9 * q^29 - 9 * q^30 - 3 * q^31 - 9 * q^33 + 9 * q^34 - 27 * q^36 + 3 * q^37 - 12 * q^38 - 18 * q^39 + 18 * q^40 + 3 * q^43 - 15 * q^44 + 18 * q^45 + 3 * q^47 + 6 * q^50 - 9 * q^51 + 42 * q^52 - 6 * q^53 - 9 * q^57 - 18 * q^58 - 3 * q^59 + 9 * q^60 + 6 * q^61 + 60 * q^62 + 24 * q^64 - 15 * q^65 + 18 * q^66 + 12 * q^67 - 12 * q^68 + 9 * q^69 + 18 * q^71 + 45 * q^72 - 21 * q^73 - 60 * q^74 + 9 * q^75 + 15 * q^76 + 54 * q^78 + 21 * q^79 - 15 * q^80 - 9 * q^82 - 18 * q^83 - 9 * q^85 + 12 * q^86 - 36 * q^87 + 54 * q^88 + 12 * q^89 - 27 * q^90 - 3 * q^92 - 27 * q^93 - 18 * q^94 + 12 * q^95 - 3 * q^97 + 18 * q^99

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